becoming a teacher: emerging teacher identity in

Helsinki 2009

Becoming a teacher:

emerging teacher identity in mathematics

teacher education

Research Report 308

Helsinki 2009

Heidi Krzywacki

Becoming a teacher:

emerging teacher identity in mathematics

teacher education

Academic Dissertation to be publicly discussed, by due permission of the Faculty of Behavioural Sciences at the University of Helsinki, in the Small Hall of the university main building, Fabianinkatu 33, on November 13th, 2009, at 12 o’clock

Supervisor: Professor Jari Lavonen University of Helsinki Assessors: Professor Arja Virta University of Turku

Associate professor Jeppe Skott Århus University

Assistant professor Peter Liljedahl Simon Fraser University

Custos: Professor Jari Lavonen University of Helsinki Opponent: Professor Douwe Beijaard Technische Universiteit Eindhoven

ISBN 978-952-10-5756-4 (nid) ISBN 978-952-10-5757-1 (pdf)

ISSN 1795-2158 Yliopistopaino

2009

UNIVERSITY OF HELSINKI

Faculty of Behavioural Sciences

Department of Applied Sciences of Education

Research Report 308

Heidi Krzywacki

Becoming a teacher: emerging teacher identity in mathematics teacher education

Abstract

This research examines three aspects of becoming a teacher, teacher identity formation in

mathematics teacher education: the cognitive and affective aspect, the image of an ideal teacher

directing the developmental process, and as an on-going process. The formation of emerging

teacher identity was approached in a social psychological framework, in which individual devel-

opment takes place in social interaction with the context through various experiences. Formation

of teacher identity is seen as a dynamic, on-going developmental process, in which an individual

intentionally aspires after the ideal image of being a teacher by developing his/her own compe-

tence as a teacher. The starting-point was that it is possible to examine formation of teacher

identity through conceptualisation of observations that the individual and others have about

teacher identity in different situations.

The research uses the qualitative case study approach to formation of emerging teacher iden-

tity, the individual developmental process and the socially constructed image of an ideal mathe-

matics teacher. Two student cases, John and Mary, and the collective case of teacher educators

representing socially shared views of becoming and being a mathematics teacher are presented.

The development of each student was examined based on three semi-structured interviews sup-

plemented with written products. The data-gathering took place during the 2005–2006 academic

year. The collective case about the ideal image provided during the programme was composed of

separate case displays of each teacher educator, which were mainly based on semi-structured

interviews in spring term 2006. The intentions and aims set for students were of special interest

in the interviews with teacher educators. The interview data was analysed following the modified

idea of analytic induction.

The formation of teacher identity is elaborated through three themes emerging from theo-

retical considerations and the cases. First, the profile of one’s present state as a teacher may be

scrutinised through separate affective and cognitive aspects associated with the teaching profes-

sion. The differences between individuals arise through different emphasis on these aspects.

Similarly, the socially constructed image of an ideal teacher may be profiled through a combina-

tion of aspects associated with the teaching profession. Second, the ideal image directing the

individual developmental process is the level at which individual and social processes meet.

Third, formation of teacher identity is about becoming a teacher both in the eyes of the individ-

ual self as well as of others in the context. It is a challenge in academic mathematics teacher

education to support the various cognitive and affective aspects associated with being a teacher

in a way that being a professional and further development could have a coherent starting-point

that an individual can internalise.

Keywords: teacher identity, pre-service teacher education, professional identity, teacher devel-

opment, mathematics student teacher

HELSINGIN YLIOPISTO

Käyttäytymistieteellinen tiedekunta

Soveltavan kasvatustieteen laitos

Tutkimuksia 308

Heidi Krzywacki

Heräävä opettajuus – opettajaidentiteetin muotoutuminen matematiikan opettajankoulutuksen

aikana

Tiivistelmä

Tutkimuksessa on tarkasteltu opettajaidentiteetin muotoutumista matematiikan opettajankoulu-

tuksen aikana kolmesta eri näkökulmasta: kognitiivisten ja affektiivisten ulottuvuuksien, kehi-

tysprosessia suuntaavan opettajuuden ihannekuvan sekä jatkuvan prosessin näkökulmasta. Tut-

kimuksessa opettajaidentiteettiä tarkasteltiin sosiaalipsykologisessa viitekehyksessä, jossa yksi-

lön kehittyminen tapahtuu vuorovaikutuksessa ympäröivän kontekstin kanssa erilaisten koke-

musten kautta. Opettajaidentiteetin muotoutuminen nähdään dynaamisena kehittymisprosessina,

jossa pyritään intentionaalisesti kohti ihannekuvaa opettajuudesta kehittämällä omia valmiuksia

opettajana. Tutkimuksen lähtökohtana on ollut mahdollisuus tarkastella opettajaidentiteettiä ja

siihen liittyviä prosesseja käsitteellistämällä sekä yksilön itsensä että muiden havaintoja identi-

teetin ilmentymästä eri tilanteissa.

Tutkimuksessa sitouduttiin laadulliseen tapaustutkimukseen, jossa opettajaidentiteetin muo-

toutumista tarkasteltiin niin opiskelijan yksilöllisen kehittymisen ja sosiaalisesti konstruoidun

matematiikan opettajuuteen liittyvän ihannekuvan näkökulmasta. Työssä on raportoitu kaksi

opiskelijatapausta, John ja Mary, sekä kollektiivinen tapauskuvaus opettajankouluttajista kuvaa-

massa sosiaalisesti jaettua näkemystä. Opiskelijoiden kehittymistä seurattiin lukuvuonna 2005–

2006 tehtyjen kolmen teemahaastattelun ja täydentävän kirjallisen materiaalin avulla. Kollektii-

vinen kuvaus koulutuksessa tarjotusta opettajan ihannekuvasta perustui erillisiin kouluttajista

tehtyihin tapauskuvauksiin, jotka perustuivat pääosin keväällä 2006 tehtyihin teemahaastattelui-

hin. Haastatteluissa keskityttiin kouluttajien intentioihin ja opiskelijoille asetettuihin tavoitteisiin.

Tutkimusaineisto analysoitiin teoriaohjaavan sisällönanalyysin suuntaisesti.

Opettajaidentiteettiä on käsitteellistetty niin teoreettisen tarkastelun kuin tapausten perus-

teella. Yksilön opettajaidentiteetin tilaa kunakin hetkenä on mahdollista profiloida opettajuuden

kognitiivisten ja affektiivisten ulottuvuuksien avulla. Yksilölliset erot voidaan nähdä osa-

alueiden erilaisina painotuksina. Yhtälailla sosiaalisesti konstruoitua ihannekuvaa matematiikan

opettajuudesta voidaan kuvata ammatillisuuteen liitettyjen piirteiden kokoelmana. Ihannekuva,

joka suuntaa yksilöllistä kehitysprosessia, nähdään yksilöllisten ja sosiaalisten prosessien raja-

pintana. Opettajaidentiteetin muotoutumisessa on kysymys siitä, että yksilöstä tulee opettaja sekä

itsensä että ympäristön silmin. Haasteena akateemisessa matematiikan opettajankoulutuksessa on

tukea erilaisten opettajuuteen liittyvien sekä kognitiivisten että affektiivisten ulottuvuuksien

kehittymistä niin, että ammatillisuudelle ja sen kehittymiselle myös jatkossa muodostuisi kohe-

rentti yksilön sisäistämä lähtökohta.

Avainsanat: opettajaidentiteetti, opettajankoulutus, ammatillinen identiteetti, opettajan ammatil-

linen kehittyminen, matematiikan aineenopettajaopiskelija

Becoming a teacher: emerging teacher identity in mathematics teacher education i

Contents

1 Introduction.................................................................................................1

1.1 Research task ......................................................................................3

1.2 The framework of ‘teacher identity’ ..................................................4

1.3 Structure of the research report ..........................................................8

2 Teacher identity in educational research...................................................11

2.1 Formation of teacher identity ...........................................................12

2.2 Teacher identity through characterisation ........................................15

3 Characteristics of teacher identity.............................................................19

3.1 Cognitive aspects..............................................................................21

3.1.1 Content knowledge ...............................................................23

3.1.2 Pedagogical content knowledge............................................25

3.1.3 Pedagogical knowledge.........................................................29

3.1.4 Thinking skills.......................................................................32

3.2 Affective aspects ..............................................................................37

4 The image of the ideal teacher directing development .............................41

4.1 Conceptions of a good teacher .........................................................41

4.2 The image of the ideal teacher from a collective perspective ..........43

4.3 The ideal image orienting individual development ..........................44

5 Teacher identity as an on-going process...................................................49

5.1 Internal processes of identity formation ...........................................51

5.1.1 Student teacher background ..................................................52

5.1.2 Becoming a teacher ...............................................................54

5.1.3 Teacher identity constructed through experience .................57

5.2 External processes of identity formation..........................................61

5.2.1 Identity as socially constructed .............................................62

5.2.2 Contextual influences............................................................65

5.3 Boundaries between internal and external........................................68

ii Heidi Krzywacki

6 Research questions ................................................................................... 71

7 The case study approach........................................................................... 75

7.1 The paradigmatic background of the research ................................. 76

7.2 Methodological choices ................................................................... 77

7.3 The role of the researcher in the research process ........................... 79

7.4 Conclusions concerning the paradigmatic background ................... 81

8 Conduct of the research ............................................................................ 83

8.1 Defining the research cases.............................................................. 83

8.1.1 Mathematics teacher education as a research context .......... 84

8.1.2 Student teachers .................................................................... 87

8.1.3 The collective case of teacher educators .............................. 90

8.2 The data-gathering process .............................................................. 95

8.2.1 Interviews ............................................................................. 96

8.2.2 Supplementary material ...................................................... 101

8.3 Data handling and analysis ............................................................ 102

8.3.1 Interview data ..................................................................... 104

8.3.2 Supplementary material ...................................................... 111

8.4 Conclusion concerning the research procedure ............................. 112

9 Teacher identity: formation through three cases .................................... 115

9.1 Student 1: John............................................................................... 116

9.1.1 Am I going to be a teacher?................................................ 116

9.1.2 The developmental process profiled through

characterization................................................................... 118

9.1.3 Identifying oneself with being a mathematics teacher ....... 128

9.2 Student 2: Mary.............................................................................. 132

9.2.1 I am going to be a mathematics teacher ............................. 132

9.2.2 The developmental process profiled through

characterization................................................................... 135

9.2.3 Identifying oneself with being a mathematics teacher ....... 145

9.3 The image of the ideal teacher provided

during the teacher education .......................................................... 150

9.3.1 The general vision of the ideal mathematics teacher.......... 150

9.3.2 The characterisation of the ideal mathematics teacher ....... 152

Contents iii

9.4 Conclusions concerning the cases ..................................................163

9.4.1 Characterisation of teacher identity ....................................164

9.4.2 Approaching teacher identity through the present and

ideal images.........................................................................165

9.4.3 The on-going process of teacher identity ............................169

10 On the trustworthiness of the research....................................................171

10.1 Triangulation ..................................................................................172

10.2 Credibility.......................................................................................174

10.3 Transferability ................................................................................175

10.4 Dependability .................................................................................177

10.5 Confirmability ................................................................................179

11 Discussion ...............................................................................................181

11.1 On the relevance of the research ....................................................181

11.2 Reflections on teacher identity formation ......................................183

11.3 Implications ....................................................................................187

11.4 Further research ..............................................................................190

REFERENCES .............................................................................................193

APPENDICES..............................................................................................203

Becoming a teacher: emerging teacher identity in mathematics teacher education 1

1 Introduction

The original motive for undertaking this research topic emerged from obser-

vations about practice in the teacher education programme. Teacher educa-

tion faces the challenge of paving the way for student teachers, who, after

many years of academic studies in disciplines like mathematics, should inter-

nalise the idea of being a teacher within a one-year educational studies. Aca-

demic teacher education is founded on the idea that through disciplinary stud-

ies designed to teach the knowledge and skills, and with the help of limited

practical experience and other interactional activities, an individual is trans-

formed into a teacher. At least, an individual is to acquire the knowledge and

skills for further development of emerging professionality (Niemi & Jakku-

Sihvonen, 2006; Westbury, Hansén, Kansanen, & Björkvist, 2005). In gen-

eral, becoming and being a professional teacher is associated with cognitive

expertise that includes the idea of knowing and mastering certain knowledge

domains as well as readiness to apply one’s own expertise in the classroom.

However, the cognitive approach is not the only perspective from which

to consider ‘becoming and being a teacher’, as Atkinson (2004) claims. Per-

sonal identification with the teaching profession, the influence of the social

environment, and the views of the teaching profession in general are also

associated with being a teacher. Taking a role as a teacher in front of the

classroom is a challenging task for many students at first. During teacher

education, teaching practice provides an opportunity to face the role as a

teacher and to have a feeling for ‘being a teacher’. Two issues have to be

addressed. Firstly, from an individual perspective, one needs to fully inter-

nalise and identify with being a teacher. Even at the beginning of the research

project, a preconception was that attainment of the true image as a mathemat-

ics teacher was not easy. Secondly, recognition by others, including pupils,

other teachers and parents, is also essential, in addition to the need for indi-

vidual internalisation. An individual needs to be seen as a teacher, to have a

position as a teacher in the view of others (Gee, 2000).

Given all this, cognitive expertise seemed to be too narrow and individu-

alistic as a theoretical basis for this undertaking, so that teacher identity has

been chosen as the main concept in examining the process of becoming a

teacher, emerging professionality. In this case study, the main purpose is to

conceptualise the professional identity of the teacher, ‘teacher identity’, and

then to explore the process of ‘becoming a teacher’ during mathematics

teacher education through this theoretical framework, foregrounding an indi-

vidual perspective for the process of ‘becoming a teacher’. In the case of

2 Heidi Krzywacki

mathematics student teachers, the interest is what process takes place when

an individual student is involved with working on the teacher’s professional

identity and takes a step towards the teaching profession during pre-service

teacher education. Since practical experiences in a school community are

limited in Finnish academic teacher education, the individual developmental

process is more about the students’ ability to imagine themselves as teachers

than about development through hands-on experience mediated by ‘real life’.

The active role and the commitment of the individual are fundamental in con-

structing professional identity as a teacher based on academic university

course. Conceptualisation of emerging teacher identity, an individual trajec-

tory towards ‘becoming a teacher’ in terms of practical notions is essential.

However, individual development takes place in close association with

the educational context. This research examines the formation of teacher

identity in Finnish pre-service teacher education. Even though the main focus

is primarily on the individual, the process of development is driven by con-

textual influences, for example, by shared conceptions of being a mathemat-

ics teacher in Finland. Firstly, the culture of trust can be seen at all levels of

Finnish education as an autonomous standpoint of teachers in school. Teach-

ers are not only those who implement the decisions of higher authorities, but

who also take responsibility for making decisions about the curriculum

through planning and writing the school-level curriculum in more detail

within national guidelines (Westbury et al., 2005). Naturally, teachers take

also responsibility for planning and implementing classroom activities and

evaluation processes. A teacher is seen as a professional who is responsible

for learning as well as for personal professional development later during his

or her teaching career (Kosunen & Mikkola, 2002). There is a need for pro-

fessional identity, truly identifying with being a teacher.

In order to educate such teachers, Finnish teacher education is designed

on the main principle of the research-based approach, which prioritizes

teacher pedagogical thinking and construction of a solid personal theory. In

other words, the teaching profession is not only based on expertise in various

disciplines but also on competence in applying such knowledge and skills to

making decisions and justifying actions in the classroom (Lavonen et al.,

2007). Furthermore, there is not simply one way to act as a good teacher but

many. Individual students seem to develop in different ways and to value

different elements subjectively. Since they experience the same kinds of ac-

tivity and interaction in teacher education differently depending on their per-

sonal characteristics, motives, and background, a need to understand the

complexity of formation of emerging teacher identity from the individual

perspective was foregrounded.

Introduction 3

‘Becoming a teacher’ includes some notions that need to be taken into

consideration in this research. On the one hand, as Beijaard, Meijer, and Ver-

loop (2004) point out, being a professional teacher is a value-bound notion.

The role that teachers have in the school system and, consequently, the skills,

knowledge, and attitude to the teaching profession needed as a teacher are

conditional on the context. Becoming and being a professional mathematics

teacher has its special features that are embedded in the Finnish educational

system and principles. Therefore, the meaning of professionality needs to be

elaborated in examining emerging professional identities of mathematics stu-

dent teachers. In this research, particular cognitive and affective aspects asso-

ciated with the teaching profession in the Finnish educational context are to

clarify the meaning of professionality. On the other hand, the interplay be-

tween individual and contextual dimensions in teacher identity formation

emerges from practical notions. Teacher identity in general is of great interest

in the educational field. Conceptualisations of teacher identity are various, as

are research approaches to the topic. In this work, the interest was to build up

a framework for teacher identity that could provide a tool for analysing the

developmental process of student teachers during their teacher education. An

individual student is considered to have an active role in the on-going identity

construction that takes place in the academic context. Altogether, teacher

identity is seen as something both personal and socially shared (e.g., Beijaard

et al., 2004; Côté & Levine, 2002).

1.1 Research task

I now describe the steps through which the aim of the research was developed

in order to help readers to understand why the research task is framed in such

a way. Qualitative case study as a research approach is a basis of this research

(Stake, 1995; Patton, 1997 and 2002). As Stake (1995, pp. 15–16) points out,

it is thus essential to frame the purpose for research clearly enough and to

keep the main focus in mind throughout the process. The research task, espe-

cially the specific questions, has been refined during the process based on

both empirical and theoretical examination.

The research topic originally emerged within the developmental process

of the mathematics and science teacher education programme at the Univer-

sity of Helsinki. Co-operation between the organisers, who represent univer-

sity departments involved with the teacher education programme, has aimed

at promoting the coherence of the programme. Along with the developmental

project, preliminary study was carried out to reveal how the study programme

4 Heidi Krzywacki

is actually implemented according to students (Krzywacki & Juuti, 2005).

The present implementation of the programme was evaluated on the basis of

student interviews and questionnaires. The evaluation information was used

for developmental work, but it also improved the researcher’s understanding

of the context of teacher education. At the time, the meaning of the educa-

tional context for student development, social processes and the evaluative

approach for teacher education were the main interests.

However, even if the educational context in which the beginning students

take their first steps towards becoming a teacher is essential, the focus of the

research was moulded to examine the nature of teacher identity more from an

individual perspective, eventually producing the idea of conducting research

on what is actually happening in understanding of student teachers during

their studies. One of the most influential factors was the notion that individu-

als develop in different ways and value different elements subjectively. They

experience the same kind of activities and interaction in their teacher educa-

tion differently, depending on their personal characteristics. A need to under-

stand the complexity of individual development within teacher education was

considered of prime importance.

This research is about becoming a mathematics teacher, the process of

emerging teacher identity, especially from the individual perspective. The

aim is to understand the early steps in constructing professional identity that

will develop further throughout the teaching career. The research task is to

examine what the process of teacher identity formation is like in math-ematics teacher education. This case study on formation of teacher identity

is limited to cases of student teachers who have mathematics as their major

and to a collective case of teacher educators representing the contextual in-

fluences on the process. The specific research questions are presented in a

separate chapter after the theoretical conceptualisation.

1.2 The framework of ‘teacher identity’

The overall framework for more detailed elaboration of teacher identity later

on in this research is now introduced. The concept of ‘identity’ is widely used

in research, although no agreed definition exists in the literature because of

the variety of disciplinary backgrounds (Beijaard et al., 2004; Eteläpelto &

Vähäsantanen, 2006; Gee, 2000). In general, since identity has been embed-

ded in various theoretical frameworks, including sociological, cultural, an-

thropological, philosophical, and psychological ones, it is natural that defini-

tions and approaches differ greatly. Consequently, it was necessary to clarify

Introduction 5

the point of departure for the overall understanding and the locus of teacher

identity.

Despite my primary interest in the individual perspective of emerging

professional identity, I regard teacher identity and its formation as an on-

going process of change embedded in the context. Teacher identity cannot in

fact be conceptualised without both perspectives, social and personal, as

Eteläpelto and Vähäsantanen (2006) claim (see also Beijaard et al., 2004). To

be able to conceptualise emerging professional identities of student teachers

and to take into consideration the notion of building identity within a particu-

lar context, there was a need to establish the research on the framework that

allows me to discuss teacher identity from individual and social perspectives.

Furthermore, since I understand professionality, in this case ‘being a teacher’,

as a context and value bound phenomenon involving both individual and so-

cially shared ideas associated with the teaching profession, the research

framework needed to address the multidimensional locus of professional

identity.

The multidimensional model of identity formation of Côté and Levine

(2002) will clarify my understanding of teacher identity in general (see Fig-

ure 1). Côté and Levine (2002) founded their theoretical model of traditions

of psychological and sociological approaches to identity on the work by Erik-

son (1968) especially. Even though they have designed the model for exam-

ining the societal viewpoint of reproduction of culture and identity in general,

it is seen as a productive starting-point for this study, addressing both social

and individual perspectives for identity formation.

Figure 1. Côté and Levine’s multidimensional model of identity formation (2002, p.

134)

Social identity (social structure)

Ego identity (personality)

context

person

Personal identity (interaction)

3

4 EXTERNAL

INTERNAL 2

1

6 Heidi Krzywacki

Identity in general, and teacher identity likewise, manifests itself at three lev-

els. As Côté and Levine (2002, pp. 131–134) describe, teacher identity for-

mation is a continuous process between ego, personal and social levels,

through which identity can be approached. The ego identity represents inter-

nal mental processes that are the basis for individual understanding of one’s

own teacher identity. This level represents the personal continuity of one’s

own understanding and that to which a person attaches previous understand-

ing, personal features and values within this on-going process. At the per-

sonal identity level, a person engages in interaction with others in a particular

context. This involves behaviour and impressions that a person presents to

others and oneself. Social identity represents a socially constructed under-

standing of reality, in this case, socially shared perceptions of being a teacher,

a social reality which influences a person and can be influenced by a person

through everyday interaction with other people. Social structures, like norms,

values, and traditions, are implemented and reproduced in concrete actions at

the personal level.

The process of identity formation is divided into four phases between the

components. The arrows between personal and ego identity components (2

and 3) represent the internal processes of teacher identity formation. A person

constructs a subjective understanding of reality, of being a teacher, based on

social influences. Not all socially shared perceptions will be automatically

internalised as part of personal understanding. The other part of internal pro-

cesses is about construction of a self-presentation as a teacher that is accords

with previous internalisations and inner understanding in growing into being

a teacher. Previous experiences have a role in this process.

The interaction between personal and social components represents the

external processes of teacher identity formation, i.e., how a person engages in

interaction with other people, and through that, is influenced by and con-

structs social reality with others. On the one hand, the relationships between

social and personal identity components (arrow 1) represent how social re-

ality influences interaction between people and through that the individual.

Actual day-to-day interaction makes it possible for a person to experience

socially shared principles and values, norms and ideals. Socialisation pro-

cesses are a key issue for teacher identity during teacher education. On the

other hand, people construct social reality and in this case, ‘teacher identity’,

the socially shared understanding of being a teacher (arrow 4), in interaction

with one another.

Particular aspects have to be considered in research on the formation of

emerging professional identity since the model is designed for analysis of

identity in general. First, teacher identity is something associated with a per-

Introduction 7

son who is becoming or is a teacher. Although the individual dimension and

psychological aspects are essential for conceptualisation, the social dimen-

sion is fundamental for teacher identity as identity formation takes place

through social interaction with others, as described in Côté and Levine’s

model (2002). In the context of teacher education, for example, mentoring in

teaching practice and various academic learning activities influence the de-

velopmental process. Consequently, identity has to be something that can be

recognised by an individual self as well as by others at particular times and

places (Gee, 2000; see also Côté & Levine, 2002). As Danielewicz (2001,

p.10) states, our understanding of who we are and who we think other people

are as well as our understanding of other people’s understanding of us is fun-

damental to teacher identity and its developmental process. It follows that the

locus of teacher identity is in both individual and social processes. Fur-

thermore, components of teacher identity (ego, personal and social identity)

are accessible through conceptualising an individual’s own understanding,

i.e., through explicating individual notions of professional identity.

Second, teacher identity is manifested through some characteristics asso-

ciated with becoming and being a teacher. As Côté and Levine claim (2002,

pp. 131–140), it is possible to recognise identity at different levels of mani-

festation, and the question of what is actually recognised is addressed through

characterisation. In this research, the focus is on teacher professional identity,

which is characterised by the features associated with the profession. Charac-

terisation makes it possible to discuss teacher identity from an individual

perspective, i.e., the individual developmental process, as well as from a

social perspective, in terms of what are seen as desirable and valuable fea-

tures of a good teacher and teaching. However, defining the essential charac-

teristics of a teacher is not possible in only one way. As Beijaard et al. (2004)

maintain, characteristics of teacher professional identity emerge from percep-

tions of individuals, those who are involved in the internal developmental

process, as well as from social perceptions by those who are involved with

the developmental process through social interaction in various contexts. Pro-

fessionalism is bounded by values and the context; in this case, the Finnish

educational system.

Third, teacher identity is seen as an on-going process, meaning that iden-

tity cannot be seen as fixed but continuously in flux and dynamic (e.g., Bei-

jaard et al., 2004; Côté & Levine, 2002). Identity is continually reshaped

through individual experiences in social interaction with others in terms of

personal identity. The processes which students are involved with can be

considered as a series of changes, as Richardson and Placier (2001) indicate,

leading towards ‘being a (good) teacher’. The whole process of change is

8 Heidi Krzywacki

embedded in interaction, and the notion of difference from and similarity to

others is essential (Danielewicz, 2001; Jenkins, 2004). However, despite the

dynamic nature of teacher identity, it is possible to recognise the state of

teacher identity at a particular time and place. Furthermore, in focusing on

the formation of emerging teacher identity, the idea is neither to describe the

situational series of changes in themselves nor to discuss isolated individual

experiences, but to capture the trends of this development and understand

professional identity. I presume that an individual has an essential role in the

process of teacher identity formation as s/he attaches values and meanings to

personal experiences (see, e.g., Beijaard et al., 2004; Sfard & Prusak, 2005),

the one who filters and possibly directs professional development towards

something better.

1.3 Structure of the research report

Finally, the structure of the research report will be described to clarify the

totality of the work. The overall framework of teacher identity has been dis-

cussed above in order to provide the understanding for the elaboration that

follows.

The theoretical part is divided into four chapters, beginning with a general

overview of educational research on teacher identity. The idea is to inform

the reader about various research approaches on this topic, and to position

this study within the research field. The next three chapters lay the founda-

tion for understanding teacher identity and its formation in this research.

First, characterisation of teacher identity is one way to approach profession-

ality and the features of the teaching profession. These characteristics allow

us to elaborate processes and states associated with teacher identity as well as

to define the meaning of being a professional teacher. Second, the signifi-

cance of the image of the ideal teacher for the developmental process is dis-

cussed. Tension between the present and designated state of individual

teacher identity can be seen as a driving force in the developmental process

(Sfard & Prusak, 2005). The ideal image is on the boundary between external

and internal processes associated with identity formation, and thus is at the

heart of developmental process. Third, on-going processes of identity forma-

tion, both internal and external, are discussed in more detail to show it as a

dynamic and continuously changing entity.

The research engages with the qualitative case study approach. A brief

conclusion after the theoretical part discusses the specific research questions.

The report continues by considering the paradigmatic background of the re-

Introduction 9

search, and then describes the conduct of the research. The teacher education

at the University of Helsinki is described in order to outline the educational

context of this research. The empirical part of the research is based on two

sources: student cases approaching the process of ‘becoming a teacher’ from

the individual viewpoint, and the collective case of teacher educators repre-

senting informants for examining the socially shared view of teacher identity.

At the end, after displaying the cases, the research questions are answered in

the section concluding the empirical part.


2 Teacher identity in educational research

This chapter reviews educational research on professional identity of teach-

ers. The review is not intended to survey the whole research area thoroughly

but to help in positioning this work in the educational field. The various

schools of educational research on teacher professional identity are of par-

ticular interest.

According to Beijaard et al. (2004), identity has been seen as socially em-

bedded trail of individual development in interaction with the environment.

The steps of personal development have been examined from the individual

perspective, particularly in regard to the characteristics of stages in the pro-

cess. According to Côté and Levine (2002), a starting-point has been the psy-

chological approach based on Erikson’s theory of identity (1968), in which

the relationship between self and identity is examined. From the individual

perspective, identity is associated with inner workings and internal processes.

Criticism of Erikson’s theory is about missing the point of social interaction,

explaining the on-going social force manipulating an individual.

The sociological viewpoint is another way to approach identity. Identity is

not owned but constructed by a person in interaction in the society that di-

rects the development (Côté & Levine, 2002; cf. Wenger, 1998). Criticism of

the sociological approach is that it lacks an empirical basis and consensus

about the nature of key issues. Côté and Levine (2002) conclude that both

perspectives are needed and their solution is the social psychological frame-

work of identity, as is the case in this research. They rationalise their theo-

retical framework with the notion that both perspectives were originally in-

fluenced by Erikson’s model, but the locus of identity differs.

Educational research thus provides no clear traditions in professional

identity either, especially teacher identity. Firstly, Korthagen (2004) points

out that the concept of ‘self’ and linking it with professional identity is prob-

lematic causing differences over common understanding of the phenomenon.

Besides, it seems that theoretical frameworks have been used in disparate

ways. Secondly, various topics are associated with the professional identity

of the teacher. According to the research review by Beijaard et al. (2004),

‘professional identity’ was associated with teacher knowledge (Arnon &

Reichel, 2007; Beijaard, Verloop, & Vermunt, 2000; Smith, 2007), profes-

sional environment (Moore & Hofman, 1988; Samuel & Stephens, 2000),

self-image and self-evaluation (Beijaard et al., 2000; Korthagen, 2004),

social structure and traditions (Coldron & Smith, 1999), and reflection, be-

side personal and social history (Antonek, McCormick, & Donato, 1997), as

12 Heidi Krzywacki

well as narratives (Connelly & Clandinin, 1999; Nelson, 2008). Furthermore,

in the narrative approach, teacher identity has been equated with stories told

by teachers (e.g., Sfard & Prusak, 2005). Altogether, the concept of teacher

identity has been defined in various ways, if defined explicitly at all.

In order to give an overview of research on teacher identity, two subsets

described by Beijaard et al. (2004) are used to structure this chapter: (1) re-

search on professional identity formation, and (2) research on identification

of the characteristics of the teacher’s professional identity. The categorisation

by Beijaard et al. (2004) was of help in examining the broad and incoherent

educational research field of teacher identity. A brief overview of how this

research is positioned in the field appears at the end of both sections. Besides,

reasons are given for structuring the theoretical part of this study based on

three themes, characterisation of teacher identity, on-going process of teacher

identity, and the importance of the image of the ideal teacher.

2.1. Formation of teacher identity

Formation of professional identity has been important in educational research

(Beijaard et al., 2004). Research on teacher change, a widely examined topic,

is considered here as one point of departure. Richardson and Placier (2001)

have distinguished two positions in research on teacher change and changes

in teaching. While the cognitive, affective, and behavioural change processes

affecting individual and small group processes have been examined, teacher

change and its cultural, structural, and political aspects has been significant

from the organisational perspective. In general, Richardson and Placier

(2001) have paid attention to issues related to defining the change: who has

the power over change and how is the change oriented during the process?

How is change defined and verified? In what direction do teachers change?

What is the process of change like? Richardson and Placier claim that, des-

pite the perspective on teacher change, instructional changes in school envi-

ronment involve both individual change in beliefs and knowledge and cul-

tural change at the organisational level (see also Coldron & Smith, 1999).

Firstly, internal processes regarding integration of the personal with pro-

fessional as well as the relationship between self and identity have been in-

vestigated (Korthagen, 2004). Teacher’s professional identity formation is

influenced by beliefs that are determined by the biographies of individuals

(Kagan, 1992; Knowles, 1992; Beijaard et al., 2004). In addition to biogra-

phies, Richardson and Placier (2001) also regard personhood and experiences

as influential factors for individual change. Consequently, the mechanism of

Teacher identity in educational research 13

promoting change is complex and, as Richardson and Placier state, research

documents the difficulties of making a deep and lasting impact on the beliefs

and conceptions of the students (see also Settlage, Southerland, Smith, &

Ceglie, 2009). Individual change can be seen as naturalistic, not determinis-

tic, and as based on individual choice and autonomy. In addition, ‘many of

the changes that are studied, such as learning from experience, may not in-

volve a completely conscious process’ (Richardson & Placier, 2001, p. 909).

Understanding internal processes is important for promoting teacher change,

at least for supporting the individual in practice. While the idea of closing the

gap between the designated and present state of teacher identity is used for

describing the developmental process in the narrative approach of Sfard and

Prusak (2005), Beijaard et al. (2004) have paid attention to the gap between

personal and professional that should not be too great so as to avoid friction

in the formation process.

Another approach to individual development is professional growth and

development during the teaching career (e.g., Kagan, 1992; Richardson &

Placier, 2001). In developmental stage theories, not only are the individual’s

former experiences and biography essential but teaching experiences in the

school context and changes in the image of self as a teacher (e.g., Grossman,

1990). Models for teacher development are based on the idea that all teachers

change through the same steps and processes during their teaching career.

However, Richardson and Placier list influential factors based on research

literature: biography, experience, context, personality, and beliefs. Similarly,

McCormack, Gore, and Thomas (2006, p. 106) emphasise the meaning of

context and experience for professional learning at the beginning of one’s

career; ‘constructing a professional identity is a complex and ongoing part of

teacher learning during and continues beyond the induction phase of teach-

ing’. Lately, research on developmental stages has favoured the more flexible

idea of multiple factors, which influence progress and shifting from one stage

to another through non-deterministic changes (Richardson & Placier, 2001).

Secondly, the interplay between internal and external, individual and so-

cial factors has been critical to research. According to Beijaard et al. (2004),

describing formation of teacher identity occurs through notions about the

nature of the process. This formation is presented as a complex, on-going

process in which an individual struggles with the tension between the per-

sonal dimensions of being a teacher and the socially structured view of teach-

ing and being a teacher (e.g., Assaf, 2008). For example, Walshaw (2004) in

her research on identity in the context of the elementary mathematics class-

room engages with post-structural ideas, taking the stance that political and

institutional processes are central to identity formation. Identity cannot then

14 Heidi Krzywacki

be defined as simply only a particularity of an individual, and it would be

seen as synonymous with the teacher’s role and function if only knowledge

and beliefs are taken into account.

Eteläpelto and Vähäsantanen (2006) highlight the significance combining

these two contrasting approaches. Both are needed, and dialogue between the

two is the way for the development of professional identity. The individual

confronts external forces compelling him or her toward professional devel-

opment (Coldron & Smith, 1999). In considering the demands of society, the

individual has to be willing and able to define his or her own strengths and

attitude towards the occupation as well as to embrace continuous construction

of professionalism. For example, Beijaard et al. (2004, p. 123) conclude that

‘identity formation is a process of practical knowledge-building characterised

by an on-going integration of what is individually and collectively seen as

relevant for teaching’.

I position this research in the notions of identity formation. Firstly, the

focus is primarily on internal processes associated with teacher identity for-

mation. As described in Côté and Levine’s multidimensional model (2002),

the ego and personal levels at which teacher identity emerges are of special

interest. Even if experience and personal features are seen as influential in the

developmental process, examination is primarily about professional growth

that student teachers are involved with during teacher education than about

defining the relationship between personal and professional (Korthagen,

2004). This relationship cannot be ignored, but is considered as influential in

the process, not the main focus. Furthermore, the developmental process

without question concerns unconscious notions, as Richardson and Placier

(2001) claim, but here, conscious understanding of the state of teacher iden-

tity and the ability to conceptualise the process are regarded as a point of de-

parture for the study.

Secondly, this research is limited to examining student development that

takes place in pre-service teacher education. Emerging teacher identity not

only concerns continuous professional development but understanding the

early steps of becoming and establishing the basis for professional develop-

ment after teacher education as well. Moreover, formation of teacher identity

is not enabled through particular developmental steps but constructed indi-

vidually in social interaction (see Richardson & Placier, 2001). Therefore, the

aim is to conceptualise the process of becoming a teacher, emerging teacher

identity, in a way that individual developmental processes in becoming a

teacher can be identified.

Thirdly, research on formation of identity highlights processes of change,

which are promoted by experiences. In this research, teacher identity is seen


as an on-going process, as a dynamic and continuously changing profes-

sional state. On the one hand, an individual engages with internal processes

that take place at ego and personal identity levels (Côté and Levine, 2002).

Change involves development towards ‘being a good teacher’ through ex-

periences, in which respect the notion of the image of the ideal teacher is

influential (the designated state as a teacher according to Sfard & Prusak,

2005). The individual has an active role in the process through recognising

his or her own state as a teacher (the present image of teacher identity) and

through becoming aware of the features that s/he considers desirable as a

teacher in the future (the image of the ideal teacher). Here, filling the gap

between the ideal and present state of teacher identity is at the heart of the

individual developmental process (see also Arnon & Reichel, 2007).

On the other hand, the on-going process is seen as the interplay between

external and internal, in Côté and Levine’s model (2002), between the social

and personal identity levels. Individual development is promoted by social

interaction, and I assume that the image of the ideal teacher is the notion that

mediates the boundary between internal and external processes. Becoming a

good teacher is the main aim. The purpose is neither to distinguish internal or

external perspectives strictly nor to claim that either perspective is more es-

sential for discussing teacher identity (Eteläpelto & Vähäsantanen, 2006;

Samuel & Stephens, 2000; Bohl & van Zoest, 2002). Wenger (1998) dis-

cusses the dual nature of identity without the need to juxtapose perspectives:

We cannot become human by ourselves; hence a reified, physiologically based no-

tion of individuality misses the interconnectedness of identity. Conversely,

membership does not determine who we are in any simple way; hence generaliza-

tions and stereotypes miss the lived complexity of identity. (p. 146)

Altogether, emerging teacher identity appears at all three levels described in

Côté and Levine’s model (2002). The on-going process emerges between the

levels and is mediated by experience. However, this research is limited to

seeing the formation of emerging teacher identity primarily from an individ-

ual perspective and to considering external processes as influential in this

process.

2.2 Teacher identity through characterisation

The other approach to teacher identity is to conceptualise it through various

characteristics. However, as Beijaard et al. (2004) note, only a little research

has been done on the characteristics of teacher identity. The teacher know-

16 Heidi Krzywacki

ledge domains needed in the teaching profession have been one means of

profiling professional identity (e.g., Bohl & van Zoest, 2002; Smith, 2007;

Hodgen & Askew, 2007). In addition, as Richardson and Placier (2001, p.

905) mention, teacher change is described in various developmental terms,

like socialisation, growth, and cognitive and affective change. They continue

that examination of teacher change has focused on processes concerning the

cognitive, affective, and behavioural features of individual teachers or groups

of people.

Beijaard et al. (2000) have profiled teacher identity using three categories

of teacher knowledge needed in the teaching profession (cf. Bohl & van Zo-

est, 2002), examining teachers’ perceptions of their expertise, i.e., how they

perceive and derive themselves as teachers through expertise in subject mat-

ter, didactics, and pedagogy. As a result of this study based on questionnaire

data, the subject teachers involved saw themselves mostly as subject matter

and didactical experts, even though professional identity was a combination

of these three categories. However, the differences among their current per-

ceptions were not related to contextual, experiential, and biographical factors,

which might have influenced their perceptions. Beijaard et al. (2000, p. 751)

state that it is challenging to clarify one’s perceptions of aspects of teacher

identity, for example, when something is taken for granted and is immune to

reflection in that sense.

Another approach is to characterise professional identity through different

aspects collectively, i.e., ‘to make explicit what the occupational group shares

or should share’ (Beijaard et al., 2004, p. 115; see also Fajet, Bello, Leftwich,

Mesler, & Shaver, 2005). Shared conceptions of being a teacher can form a

norm for being a good teacher. This kind of research is related to educational

policy and documents for directing national education, for example, in the

Netherlands or England (Coldron & Smith, 1999; Korthagen, 2004), and

identity formation through social interaction (J. Cohen, 2008). Beijaard et al.

(2004) claim that, partly because of not explicitly defining ‘teacher profes-

sional identity’, aspects, roles, and characteristics related to this varies a lot.

From the collective perspective then, professional identity is seen as a collec-

tion of aspects relevant to becoming and being a teacher in general.

The characteristics of teacher identity have been researched by connecting

individual and social perspectives. Bohl and van Zoest (2002) have situated

aspects of individual teacher identity, which they call self-in-mind, within

varied communities of practice as socially-embedded self-in-community.

Their starting-point in developing a unit for examining teacher development

is both the socio-cultural background as well as teacher knowledge, which

forms a central part of mathematics teacher learning (cf. Carlsen, 1999). Ac-


cording to Bohl and van Zoest (2002), a cognitive-social continuum is needed

to provide a broader understanding both former research on different types of

teacher knowledge and learning as socially situated action. They take

Wenger’s social theory of learning and identity construction (1998) as a

framework of their study. Besides, given Shulman’s division of teacher

knowledge (1987), they address a need to have explicit and concrete dimen-

sions of teacher learning. The change in teacher identity is seen as the result

of learning through interaction with others; for example, based on getting

feedback, adjusting one’s own beliefs to align those of the school com-

munity, or trying to change the practices of the community.

In this research, as Beijaard et al. (2004) suggest, the characteristics of teacher identity are defined both individually and collectively. In Côté and

Levine’s model (2002), characterisation is the way to make the notions of

teacher identity approachable in the on-going process of identity formation.

The range of characteristics associated with being a professional teacher is

constructed under the influence of contextual values and the educational

structures. The image of the ideal teacher at the boundary of external and

internal processes is seen as a range of desirable characteristics particularly

associated with a good teacher.

From the collective viewpoint, teacher identity emerging at the social

identity level in Côté and Levine’s model (2002) is seen as shared under-

standing of what is seen as valuable characteristics of a good teacher and

teaching. In this research, the basis for framing these characteristics is teacher

knowledge and knowledge-building that can be considered as fundamental to

being a professional teacher (e.g., Beijaard et al., 2000; Hodgen & Askew,

2007). The main reason for this is Finnish teacher education, which high-

lights the importance of academic competence, professional knowledge, and

the skills needed in taking the moral responsibility for education.

However, even if mastering several domains of teacher knowledge is seen

as the main source of being a professional teacher in the Finnish educational

community, individuals stress characteristics differently depending on their

personal values and experiences. In previous research on teacher identity,

characterisation has been mainly based on cognitive aspects of becoming and

being a teacher. However, since cognitive characteristics are not enough to

define the individual’s internal processes in which subjective and affective

viewpoints arise (Atkinson, 2004; Hodgen & Askew, 2007), affective aspects

associated with teacher identity are also addressed in this research. Here,

formation of emerging teacher identity is made approachable through de-

scribing the notions of teacher identity in both their affective and cognitive

characteristics.


3 Characteristics of teacher identity

In the present research, teacher identity is seen as the flexible and continu-

ously reconstructed state of being a teacher, as in Côté and Levine’s model

(2002). However, the processes and phases of emerging teacher identity re-

garding the present state of teacher identity as well as the ideal image of a

good teacher can be described through various characteristics. Besides, char-

acteristics allow us to define what it means to be a professional mathematics

teacher in general. As teacher identity is recognised both individually and

collectively, definitions of its relevant characteristics differ, depending on

person and context (Beijaard et al., 2004). In the present research, the struc-

ture of the teacher education programme as well as a review of existing re-

search literature has influenced the way the division of characteristics is for-

mulated. Finnish teacher education, especially the division of the courses and

teaching practice periods as well as academic approach to support individual

development has been influential in structuring the theoretical part of charac-

terisation of teacher identity. This division has helped understand the forma-

tion of teacher identity within this particular educational context.

Teacher identity can be recognised and profiled through cognitive and af-

fective aspects essential to being a mathematics teacher (Fajet et al., 2005;

see also Beijaard et al., 2000). In this research, teacher knowledge domains

form a starting-point for characterising being a professional teacher (see e.g.,

Carlsen, 1999; Hashweh, 2005; see also Shulman, 1987). Teacher knowledge

domains are a way to discuss emerging teacher identity, especially from the

viewpoint of the knowledge and skills that a mathematics teacher should ac-

quire during teacher education. In addition to these cognitive aspects, subjec-

tive viewpoints on becoming and being a teacher like personal feelings and

motivation are relevant (e.g., Atkinson, 2004; Eagly & Chaiken, 1993;

Hodgen & Askew, 2007; Weissglass, 1993). However, the division into cog-

nitive and affective aspects and the role of subjectivity need to be clarified.

There seems to be a general understanding of the importance of affective

aspects in teaching and learning. However, no common theory exists, which

causes an immense variety in the conceptualisation used in educational re-

search. Emotions are usually distinguished from motivation (e.g., Hannula,

2004; Hoekstra, Beijaard, Brekelmans, & Korthagen, 2007), and emotional

reactions associated with personal aspects of teaching have been stressed, like

willingness to act in certain way, situational reactions, values, and attitudes

(see Eteläpelto & Vähäsantanen, 2006; Hargreaves, 1998). In addition to dif-

ferences in the theoretical framework, research contexts vary as well. Affec-

20 Heidi Krzywacki

tive aspects have been examined from the viewpoint of learners, for example,

as a part of a self-regulative system in learning (Boekaerts, 1999; Hannula,

2004) as well as from the perspective of the teacher and professionalism

(Hargreaves, 1998; Hodgen & Askew, 2007; Korthagen, 2007). As this re-

search concentrates on emerging teacher identity, these ‘non-rational’ aspects

(after Atkinson, 2004) of the teaching profession in general as well as situ-

ational emotions that arise through personal experiences of teaching need to

be taken into account. Here, the division into three different but related sys-

tems, cognition, motivation, and emotions, through which regulation of be-

haviour and relationship with the environment is understood, forms a clear

starting-point for discussing the characteristics of teacher identity and its

formation (Hannula, 2004; see also Hoekstra et al., 2007; Schutz & DeCuir,

2002; cf. Fajet et al., 2005).

According to Hannula (2004, p. 35), ‘cognition codes information about

self and environment. It is embodied in neural connections of the brain, and

abstract thought is based on metaphors’. In the context of teacher identity,

expertise in particular knowledge domains and the ability to apply this know-

ledge in practice is seen as essential to fulfil the requirements of a profes-

sional. The state of mathematics teacher identity can be characterised accord-

ing to various cognitive aspects based on domains of teacher knowledge

(Beijaard et al., 2000; Bohl & van Zoest, 2002; Smith, 2007). In order to

keep the outline of knowledge domains sufficiently clear, teacher knowledge

is divided into three main subsets proposed originally by Shulman (1987) (cf.

Grossman, 1990; see also Carlsen, 1999). For example, Beijaard et al. (2000)

understands teacher identity as associated with professional knowledge in

terms of expertise in subject matter, pedagogical, and didactical issues (see

also Bohl & van Zoest, 2002).

In addition to the domains of teacher knowledge, meta-cognitive skills

form a subcategory of cognitive aspects of teacher identity. Cognitive aspects

are not only understood as knowledge of and about something but as skills

related to specific content, including the ability to express oneself, to act and

to reflect on the cognitive aspects of teaching (Walkington, 2005). Finnish

teacher education in particular emphasises the idea that all teachers should be

able to think analytically for further self-development and to apply their

knowledge in dynamic situations (Niemi & Jakku-Sihvonen, 2006; Lavonen

et al., 2007).

Affective aspects that are also crucial for the teaching profession can be

used in characterising the state of teacher identity (e.g., Atkinson, 2004).

Hannula (2004, p. 35) defines the second category, motivation, as ‘the ener-

gizing principle for human behaviour, originating from needs, and repre-

Characteristics of teacher identity 21

sented in a hierarchically organised structure of needs and goals’. Needs are

seen as the basis of motivation. A person directs him/herself towards and

commits to something; for example, becoming and being a teacher. The third

category, emotions, ‘code information about progress towards personal

goals…’, as Hannula (2004, p. 35) continues. In other words, emotions are

understood as situational and momentary, and are associated with situations

that an individual experiences (Schutz & DeCuir, 2002; see also Korthagen,

2007). Affective aspects associated with the teaching profession in general

(being a teacher) have to be distinguished from the viewpoint of the on-going

formative process based on series of experiences in particular situations (be-

coming a teacher) described in Côté and Levine’s model (2002). Therefore,

affective aspects of teacher identity include motivation (after Hannula, 2004)

as well as subjective characteristics describing the state of emerging teacher

identity or the general view of being a good mathematics teacher (Fajet et al.,

2005). Emotions are discussed in the context of an on-going formation pro-

cess associated with experience that promotes the change.

In what follows, I discuss two subsets of characteristics, the cognitive and

affective aspects associated with teacher identity emerging during teacher

education. First, three main knowledge domains, content knowledge, peda-

gogical content knowledge, and pedagogical knowledge, as well as the cate-

gory of thinking skills comprise the basis for cognitive characterisation. This

division is in accordance with the structure of the teacher education pro-

gramme (described in more detail in the ‘Conduct of the research’ chapter)

and with the aims that are set for prospective teachers. Second, affective as-

pects are elaborated in more detail in addition to cognitive aspects. When

focusing on the early steps of teacher identity formation especially the affec-

tive notions, for example, a need to commit to the teaching profession and an

ability to identify with being a teacher arise.

3.1 Cognitive aspects

The theoretical framework for aspects of teacher identity is founded on the

concept of ‘teacher knowledge’, which is widely researched but forms an

incoherent entity (Gess-Newsome, 1999b; see also Berry, Loughran & van

Driel, 2008). Teacher knowledge and special domains of professional know-

ledge have been widely discussed in recent years from the viewpoint of

teaching and educational research, as Gess-Newsome (1999a) states. On the

one hand, research on teacher knowledge has been about domains of know-

ledge, such as content knowledge in specific disciplines like mathematics

22 Heidi Krzywacki

(e.g., Ball & Bass, 2000; Kahan, Cooper, & Bethea, 2003). The structure of a

teacher’s knowledge base, especially the role of content knowledge and

pedagogical content knowledge, identifies secondary teachers in specific sub-

jects, and is the basis of professionality (Gess-Newsome, 1999b; see also

Berry et al., 2008). In addition to content knowledge, pedagogical content

knowledge has been of special interest since Shulman’s argument concerning

the ‘missing paradigm’ (1986; 1987). That pedagogical content knowledge is

the domain that distinguishes and identifies teachers from experts on content

(Shulman, 1987). On the other hand, the origin of teacher knowledge has also

been of interest. For example, Hiebert, Gallimore, and Stigler (2002) have

examined the epistemological features of teacher knowledge by distinguish-

ing between knowledge constructed in practice and knowledge based on edu-

cational research. D. Cohen (2008) discusses the requirements that teacher

knowledge should meet the need to make a teacher’s expert knowledge ac-

cessible to learners.

The structural perspective for teacher knowledge is based on domains

such as content knowledge, pedagogical content knowledge and general

pedagogical knowledge, and distinctions between them (Carlsen, 1999;

Hashweh, 2005; see also Shulman, 1987). In general, teacher knowledge has

been conceptualised in many ways and categories of knowledge have varied,

starting from Shulman’s structural model (1987) in which pedagogical con-

tent knowledge, content knowledge apart from knowledge of curriculum

were all included in the domain called ‘content knowledge’. Later, for exam-

ple, Hashweh (2005) introduced a model of pedagogical constructions as a

substitute for pedagogical content knowledge. His model develops these con-

structions based on solid knowledge categories through repeated planning

and practical experience.

The structural model of teacher cognitions has its disadvantages, like be-

ing static, rigid, and systemic without taking individual differences into ac-

count. Neither are the cognitions of teachers such as the ability to make

pedagogical decisions addressed in structural models (Carlsen, 1999; cf.

Hashweh, 2005). However, the model does provide established and clear

categories through which individual development and emerging teacher iden-

tity is possible to profile. Teacher knowledge based on Shulman’s original

model (1987) is seen as essential for teacher identity (as in Beijaard et al.,

2000; Bohl & van Zoest, 2002; Smith, 2007). Smith (2007), as well as Bei-

jaard et al. (2000), considers expertise in knowledge as a part of being a pro-

fessional, teacher identity. Smith (2007) starts with the idea of developing

teacher knowledge and identity in interaction with each other, suggesting that

identity work should be seen as related to knowledge growth, not as an alter-


native. In this research, different knowledge domains provide a structure

through which enables examination of the individual development in accord-

ance with the structure of this particular teacher education programme.

As Gess-Newsome (1999a) points out, research on teacher knowledge is

not a coherent field. Terms relating to teacher knowledge, like knowledge,

conceptions, attitudes and values, are used inconsistently. According to Bohl

and van Zoest (2002), since not only development of knowledge in different

domains but the development of beliefs, commitments and intentions with

regard to the domains which are important for teacher identity, neither there

is need to make a special distinction between these concepts in this research.

Knowledge areas and contents that a person has a view of, knows about or

entertains beliefs about are of importance. An individual does not necessarily

distinguish between the quality of interrelation with certain epistemological

domains during the developmental process (see also Foss & Kleinsasser,

1996). Furthermore, as Bohl and van Zoest (2002) claim, response in practi-

cal situations and justification for actions are embedded in various dimen-

sions, like knowledge, intentions, commitments, and beliefs, and the relations

between them.

3.1.1 Content knowledge

Expertise in content knowledge is a special competence for subject teachers

in secondary and upper secondary schools (Gess-Newsome, 1999b; see also

Danielewicz, 2001). The meaning and definition of content knowledge differ

slightly in educational research on teacher identity. Bohl and van Zoest

(2002, p. 140) unite content knowledge with curricular knowledge, which

they call the ‘content area and curriculum dimension’, as it deals with what is

to be taught in school mathematics (cf. Grossman, 1990). Beijaard et al.

(2000), as well as Smith (2007), however, have examined teachers’ percep-

tions of their professional identity through three main knowledge domains

based on Shulman’s original model (1987). Despite the slight differences,

knowledge of subject matter is traditionally seen as a relevant part of a

teacher's professional knowledge base (Bromme, 1995; Gess-Newsome,

1999b), and thus, as an integral part of teacher identity. Furthermore, research

knowledge about teachers’ subject matter understanding can be divided into

sub-categories as Gess-Newsome (1999b) has done. According to her, ap-

proaches to content knowledge as a part of professional knowledge are (1)

conceptual knowledge, (2) subject matter structure, (3) the nature of the dis-

cipline, (4) content-specific orientations to teaching, and (5) contextual influ-

24 Heidi Krzywacki

ences on curricular implementation. The distinction between the various

categories is not easily defined, however.

The teacher’s expertise in content knowledge is central in teacher identity

formation. According to Hodgen and Askew (2007), all teachers should have

a well-established relation with what they teach. A positive relationship with

mathematics itself is of importance (see also Smith, 2007). Their study fo-

cuses on the identity of primary school teachers who seemed to struggle be-

tween the caring and nurturing aspects of identity and the strong disciplinary

focus of mathematics. They conclude that developing a strong disciplinary

bond is also crucial for primary student teachers in teaching any subject.

Teachers should therefore have opportunities to explore their identities as

mathematics teachers and learners and to develop both disciplinary intimacy

and integrity (Hodgen & Askew, 2007). Similarly, Smith (2007) has exam-

ined primary school teachers and their teacher identity development in rela-

tion to knowledge growth. Growth in content knowledge, science in his

study, is significant for development of teacher identity and differs between

individuals.

Expertise in content knowledge seems to be linked with the credibility of

a teacher. According to Beijaard et al. (2000), teachers derive their profes-

sional identity from how they see themselves as experts in various knowledge

areas. In their study, teachers who perceived themselves as subject matter

experts thought that it was not possible to be an authority for their students

and a believable professional without solid content knowledge. Burn (2007)

has considered the teacher’s relationship with content knowledge from the

viewpoint of certainty in acting as a teacher. Student teachers face a chal-

lenge to their sense of being a subject specialist and knowledge about the

subject itself during teacher education. According to Burn (2007), uncertainty

about one’s existing understanding of content itself is especially problematic

for those student teachers who regard themselves as subject specialists (cf.

Merenluoto, 2003).

The role of mathematical knowledge in good teaching has been acknow-

ledged and widely discussed in previous years (e.g., Leinhardt & Smith,

1985; Steele, 2005). Research on knowledge and beliefs about the content

knowledge of secondary teachers and its impact on the teaching process have

been of general interest, even though the connection is difficult to demon-

strate (Gess-Newsome, 1999b; Kahan et al., 2003). For example, mathemati-

cal competence is seen as a capacity for implementing curricular coherence,

i.e., teaching mathematics to coherent and significant mathematical curricular

goals (Ferrini-Mundy, Burrill, & Schmidt, 2007). However, it seems to be

difficult for teachers to combine good teaching and mathematical knowledge


(Mosenthal & Ball, 1992). Grossman (1990) mentions that the dominance of

content knowledge is so strong for some teachers that being a good teacher is

isomorphic with conceptions of knowledge in subject matter (see also D.

Cohen, 2008). However, student teachers are compelled to rethink content

knowledge from the pedagogical perspective after embarking on becoming a

teacher. Mathematics in particular induces strong views of it and about it.

Foss and Kleinsasser (1996) discussed how demanding it is to influence pre-

service teachers’ views of mathematical content knowledge as their personal

history and beliefs are so strong. As Ball and Bass (2000) claim, practical

experience is important in putting mathematical knowledge to use and for

learning to use it in teaching.

In this research, expertise in both procedural and conceptual mathematical

knowledge is essential to being a qualified professional mathematics teacher,

and to emerging teacher identity (Beijaard et al., 2000; Smith, 2007). In Fin-

nish teacher education, students should be able to build up a solid knowledge

base in mathematics through courses that they take in university mathemat-

ics. Studies in university mathematics traditionally constitute a powerful in-

fluence on the developmental process as a teacher (cf. Beijaard et al., 2000).

Mathematical education aims at basic procedural and conceptual knowledge

in mathematics and, furthermore, boundaries between the content of school

mathematics and university mathematics are not particularly addressed dur-

ing mathematical studies. Here, the distinction between mathematical know-

ledge for teaching and for other needs is not particularly made, because from

the viewpoint of emerging professional identity, the meaning of expertise in

mathematical knowledge is individually defined.

3.1.2 Pedagogical content knowledge

Pedagogical content knowledge (PCK) is regarded here as a special domain

of teacher knowledge, based in the work of Shulman (1986, 1987) and of

some researchers inspired by him (e.g., Berry et al., 2008; cf. Grossman,

1990). Shulman (1987) states that knowledge specifically associated with

teaching and learning particular subject is called pedagogical content know-

ledge.

Gess-Newsome (1999a) finds that pedagogical content knowledge has

many useful features. It has provided an analytical tool for examining teacher

cognition, highlighted the meaning of content knowledge and its transforma-

tion for teaching, and provided a more integrated vision of teacher knowledge

and classroom practice. However, it is neither an exact model nor without

26 Heidi Krzywacki

problems regarding heuristics. Gess-Newsome introduces two approaches for

conceptualising teacher knowledge. First, pedagogical content knowledge is

explained in the integrative model by the intersection of three other know-

ledge domains: content knowledge, pedagogy, and context. Thus, pedagogi-

cal content knowledge does not exist on its own (Hashweh, 2005; see also

Bromme, 1995). Second, in the transformative model, pedagogical content

knowledge is a unique form of knowledge that impacts teaching practice.

Thus, PCK is a knowledge domain which synthesises all knowledge needed

for teaching and learning (Grossman, 1990; McCaughtry, 2005; Nilsson,

2008).

Teacher cognition is not the only approach to pedagogical content know-

ledge. In his critical analysis of research on pedagogical content knowledge,

Bromme (1995) extends the original Anglo-American approach to PCK by

dividing it into two categories. Firstly, aiming at a descriptive reconstruction

of successful classroom instruction is the main idea in classical research on

teacher effectiveness. This kind of research focusing on the ‘wisdom of prac-

tice’ is embedded in normative premises regarding the objectives of teaching.

Secondly, research has been about reconstruction of the teacher competence

that is seen as professional knowledge, including pedagogical means and

tools as well as criteria for making decisions. Furthermore, Bromme (1995)

assets that an explicit conceptual distinction should be made between the

concepts of scientific disciplines, school subjects, and subject didactics.

Teachers should possess a solid professional knowledge base to be expert

teachers, despite the way professional knowledge is defined (Gess-Newsome,

1999b). Furthermore, applying knowledge in practice is essential for the

teaching profession (Bromme, 1995; Grossman, 1990; Hashweh, 2005;

McCaughtry, 2005; D. Cohen, 2008), during pre-service teacher education

(Nilsson, 2008). Grossman (1990) has examined how student teachers con-

struct pedagogical content knowledge with the help of teacher education pro-

grammes, raising the question of whether students apply their knowledge in

the classroom. McCaughtry (2005) also states that entering the classroom for

the first time and confronting the meaning of social context and interaction is

a critical factor in pedagogical content knowledge. The theoretical perspec-

tive has predominated before teaching experiences, but knowing students and

thinking about teaching in practice make a difference (see also Hashweh,

2005; Smith, 2007). Contextualising the professional knowledge and the role

of experience are important for PCK (Bromme, 1995). As Foss and Kleinsas-

ser (1996) mention, decisions in social and practical situations are made

based on conceptions of teaching and learning mathematics that are devel-

oped through experience.


Hashweh (2005) also underlines the meaning of knowledge integrated

with practice, presenting a model of pedagogical content knowledge that is an

outcome of continuous processes of planning and teaching. He calls the

knowledge domain ‘teacher pedagogical constructions’ (TPC) instead of

pedagogical content knowledge. For him, pedagogical content knowledge is

event-based and story-based constructions interconnected with practice and

experiences, not a ready-made knowledge category (see also Gess-Newsome,

1999b; cf. Grossman, 1990). Hashweh (2005) defines TPC based on tradition

of pedagogical content knowledge:

PCK is the set or repertoire of private and personal content-specific general

event-based as well as story-based pedagogical constructions that the experi-

enced teacher has developed as result of repeated planning and teaching of, and

reflection on the teaching of, the most regularly taught topics (p. 277).

Thus, pedagogical constructions are developed through teaching practice

including continuous planning and teaching activities. Teacher pedagogical

constructions (TPC) are based on seven assertions: (1) PCK represents per-

sonal and private knowledge that can be transformed into public knowledge

and shared with others; (2) PCK is a collection of teacher pedagogical con-

structions: it is not well organised and hierarchically ordered like content

knowledge, but is composed of a set of entities or smaller units; (3) TPC re-

sult mainly from planning and teaching activities; (4) TPC result from an

inventive process that is influenced by the interaction between teacher know-

ledge and belief categories; (5) pedagogical constructions constitute both a

generalised event-based and story-based kind of memory. In other words,

teacher knowledge which is both semantic and event-based distinguishes

separate components and disconnects events in order to be able to reattach

them in new way. At the same time, we might recall things narratively in

sequence, probably through analogies; (6) pedagogical constructions are topic

specific; and (7) TPC should be labelled so as to be related to other categories

of teacher knowledge and beliefs.

Similar to the content knowledge domain, pedagogical content knowledge

is related to teacher identity formation. For example, Bohl and van Zoest

(2002) have merged PCK and pedagogical knowledge together as one aspect

of ‘self-in-mind’ to make up the cognitive portion of a person’s identity.

Similarly, Smith (2007) focuses on how professional identities are developed

from the viewpoint of building pedagogical content knowledge. He has ex-

amined specific experiences of learning and teaching science in relation to

the narratives about themselves as becoming professionals. Content know-

ledge seemed to be extended during the programme, but in order to be able to

28 Heidi Krzywacki

develop pedagogical content knowledge in parallel, experience is needed to

apply knowledge in practice (see also D. Cohen, 2008; Hashweh, 2005; Nils-

son, 2008).

The role of a teacher in the classroom is seen in relation to teacher know-

ledge. For example, Goos (2005) has examined PCK from the perspective of

development of teachers’ pedagogical identities regarding technology use in

mathematics teaching and learning. In the study by Beijaard et al. (2000), the

‘teacher as a didactical expert’ is one of the three expertise roles that teachers

can identify themselves with. Similarly, Burn (2007) has examined how

learning of certain skills and knowledge affects the image of teacher identity.

She states that it is important to acknowledge existing understanding and

expertise of student teachers as subject specialists, to test and evaluate criti-

cally but not to condemn the knowledge that students bring with them into

teacher education. However, Burn (2007, p. 461) discusses the need for ‘a

sense of identity in which expertise is seen as residing not merely in their

accumulative craft knowledge …but also in their capacity to generate new

professional knowledge’. Likewise, Loughran, Mulhall, and Berry (2008)

have approached development of PCK through the idea that PCK could be

introduced explicitly, meaning that promoting student teachers’ understand-

ing of PCK as a construction reshapes their further development as teachers.

In this research on teacher identity formation, pedagogical content know-

ledge is meaningful for two reasons. Firstly, as Smith (2007) states, building

and constructing a knowledge base is associated with development of teacher

identity. Pedagogical content knowledge is considered as something that can

be taught in teacher education but still has to be constructed and internalised

by the individual (see Bromme, 1995; Hashweh, 2005; Loughran et al.,

2008). In the Finnish teacher education programme, the structure of PCK is

closer to the transformative than the integrative model (Gess-Newsome,

1999a). Students take courses in separate knowledge areas, such as math-

ematics and general education as well as in mathematics education to obtain

special knowledge about teaching and learning mathematics. Secondly, peda-

gogical content knowledge can be considered not only as teacher cognition

based on separate knowledge domains but also as teaching competence

(Bromme, 1995). A teacher has to be able to apply professional knowledge in

practice and rationalise decision-making in the classroom. Pedagogical con-

tent knowledge is associated with a person’s view of his or her own compe-

tence, and through that, with the image of self as a teacher in practice (Bei-

jaard et al., 2000).


3.1.3 Pedagogical knowledge

The third category of teacher knowledge is pedagogical knowledge of educa-

tion in general, for example, about learners and learning, the curriculum and

instruction, and classroom management (Grossman, 1990). In Shulman’s

model of teacher knowledge (1987, p. 8), the category of general pedagogical

knowledge is described as ‘knowledge, with special reference to those broad

principles and strategies of classroom management and organization that ap-

pear to transcend subject matter’. However, Morine-Dershimer and Kent

(1999) point out that the nature of pedagogical knowledge is complex. In

their model, pedagogical knowledge is grounded on the knowledge of learn-

ers and learning as well as of goals and assessment. Furthermore, they em-

phasise that the latter together with content knowledge are the basis for curri-

culum knowledge as a separate category. The category of general educational

context is connected to knowledge of specific contexts which is linked fur-

ther with pedagogical content knowledge (see also Grossman, 1990).

The other approach to the teacher’s pedagogical knowledge is to consider

facets of knowledge regarding the forms of teacher knowledge, i.e., the di-

lemma of the way of knowing and the origin of teacher knowledge. Morine-

Dershimer and Kent (1999) argue the particular importance of

interplay between general pedagogical knowledge, which is derived from the re-

search and scholarly literature, and personal pedagogical knowledge, which is

fuelled by personal beliefs and personal practical experience (p. 22).

In their review of educational research on this area, general pedagogical

knowledge consists of (1) classroom management and organisation, (2) in-

structional models and strategies, and (3) classroom communication and dis-

course. Personal pedagogical knowledge is divided into two subcategories,

personal beliefs and perceptions, and personal practical experience.

Likewise, Hiebert et al. (2002) separate professional knowledge from

practical knowledge in reference to the origin of knowledge and features of

knowledge based on its origin. The main idea of considering the facets of

teacher knowledge is to address the needs of teachers and student teachers;

i.e., to present research knowledge in a form in which teachers could adapt its

ideas in practice and as a part of their professional knowledge. (see also D.

Cohen, 2008) The challenge is in translating research knowledge into the

teacher’s reality, into school practice. This kind of knowledge is seen as an

essential element of teacher’s professional knowledge. However, as Morine-

Dershimer and Kent (1999) maintain, it has to be supplemented, applied, and

strengthened by practical, personal pedagogical knowledge. After all, teach-

30 Heidi Krzywacki

ers are practitioners who develop practical knowledge in response to practical

problems and notions in the classroom (Hiebert et al., 2002). Knowledge is

not strictly limited to the category of general pedagogical knowledge, but in

educational research, issues associated with it are typically related to peda-

gogy.

The gap between theory and practice is a special issue to be addressed

with teacher’s pedagogical knowledge. The pedagogical knowledge provided

in educational courses is based on research knowledge which is accused of

being theoretical. In addressing and understanding the needs of students and

teachers, research has been done on the views of prospective and practising

teachers on educational knowledge (e.g., Joram, 2007; Gore & Gitlin, 2004).

Gore and Gitlin (2004) state that teachers dismiss academic research on the

grounds that it is not practical, contextual, credible, or accessible. The trans-

ferability of research knowledge into the classroom environment seems to be

low. In addition, even those student teachers who valued research for its con-

tribution to on-going professional growth questioned its use in practice. The

supplementation and application of theoretical knowledge do not take place

in practice (Morine- Dershimer and Kent, 1999).

Likewise, Joram (2007) has examined the significance of epistemological

issues for educational knowledge and its the legitimacy. First, she states that

it is known that educational research is problematic part of teacher education

(see also Holligan, 1997; Korthagen, 2007). One way to rise to the challenge

is to make pre-service teachers carry out their own action research projects

during teacher education (Gore & Gitlin, 2004). However, Joram (2007)

points out that understanding epistemologies underlying the beliefs about

educational knowledge of pre-service and practising teachers as well as pro-

fessors is another way to address the problem. From the viewpoint of student

teachers, educational knowledge was non-generalizable because of a lack of

opportunity to compare a particular method in two or more classroom con-

texts (cf. Gore & Gitlin, 2004). In addition, professors as academics and pre-

service teachers encoded classroom situations differently, as professors found

certain situations to be similar in particular attributes but pre-service teachers

did not. These findings recall the observations about differences in the know-

ledge of learners and teachers by D. Cohen (2008).

Experience seems to influence the stances of teachers on educational

knowledge and its verification (Joram, 2007; Morine-Dershimer & Kent,

1999). An individual can falsify knowledge about teaching and learning, as

Joram (2007) maintains; for example, knowledge about a particular teaching

method, through personal experience of using it. However, she continues that

even if a method is found to be effective, reasoning is limited to this particu-


lar situation of their experience. The gap between research and practice could

be narrowed by building learning communities in which the focuses could be

interconnected (Korthagen, 2007; see also Wenger, 1998). Joram (2007) also

highlights the idea of being aware of the ‘culture of thinking’ by those who

are involved with teacher education. General educational knowledge could be

constructed by integrative discussions about field experiences.

Pedagogical knowledge and expertise in that particular knowledge do-

main is related to teacher identity (Beijaard et al., 2000 and 2004; Bohl & van

Zoest, 2002). However, just as definitions of pedagogical and educational

knowledge differ, this particular knowledge domain is interconnected with

professional identity in various ways. Bohl and van Zoest (2002) have com-

bined general pedagogical knowledge with PCK and knowledge of learners

into the domain called the ‘pedagogical dimension’. For them, the pedagogi-

cal dimension relates to the competencies required for arranging classroom

activities to optimize student learning. Beijaard et al. (2000) take note of

ethical and moral features that link the didactical and pedagogical sides of

teaching with each other. For them, pedagogical expertise relates to teacher’s

personal and professional role conception (see also Hodgen & Askew, 2007).

They argue that teaching is not only about technical solutions leading to

learning outcomes but about norms and values related to the teaching profes-

sion through interaction with students. Perceptions of the teacher’s role as a

facilitator of learning have also affected how the teaching profession is seen

in general.

The notion of professional development can highlight the significance of

pedagogical knowledge for teacher identity. The study by Pendry and Hus-

bands (2000) concerned secondary student teachers who were expected to

familiarise themselves with educational research. Students gave some reasons

for educational research being useful for their professional development.

First, it was practical in the sense that students found research knowledge

helpful for classroom implementation. Second, they regarded it as valuable

for prompting reflection and thinking as a teacher (cf. Holligan, 1997). Al-

though only a minority of students identified research findings as positive for

their professional development, they did not universally reject such know-

ledge. Other sources of development, like teaching practice, were seen as

more important, however. (Pendry & Husbands, 2000) Holligan (1997) states

that the role of theory as a tool in allowing the autonomous professional to

adopt a critical stance is problematic, instead theory being used to confirm

the views of practicalities and the intellectual scope that students already

have.

32 Heidi Krzywacki

In this research, pedagogical knowledge consists of two categories, gen-

eral and personal, according to Morine-Dershimer and Kent (1999) (see also

Hiebert et al., 2002). This division depends not only on the origin of know-

ledge but also content that is regarded as pedagogical. Pedagogical know-

ledge may be gained through research activities and reading literature as well

as through experiences in the classroom, e.g., through social interaction with

pupils. The idea of being able to apply and supplement general theoretical

knowledge with personal knowledge based on practical experience is essen-

tial in the teacher education programme. All kinds of pedagogical skills are

included in this category. Secondly, pedagogical knowledge is a special

knowledge domain as knowledge building is partly based on practical experi-

ence. The issues of verification of knowledge are crucial to pedagogical

knowledge. Thirdly, in addition to pedagogical content knowledge, peda-

gogical knowledge in particular orients students towards becoming a teacher.

Knowledge about teaching and learning is clearly related to one’s future pro-

fession, and hence has a special role in teacher identity formation.

3.1.4 Thinking skills

The fourth cognitive aspect of describing teacher identity formation is cogni-

tive thinking skills. Firstly, as Beijaard et al. (2004) conceptualise profes-

sional identity, practical knowledge building according to what is seen as

relevant for the teaching profession, from both an individual and collective

perspective, is essential for teacher identity formation. When teacher know-

ledge is a basis for defining professionality as a teacher, i.e., the knowledge

and skills that a teacher should master, this also leads to the question of how

to obtain and use this knowledge. Cognitive thinking skills are thus part of

becoming a professional teacher. The second reason is associated with educa-

tional politics and the common conception of a good teacher in the Finnish

educational system (Kosunen & Mikkola, 2002; Lavonen et al., 2007). A

teacher is considered to be capable of thinking and using a personal know-

ledge base for making decisions about teaching and learning. Beside this, the

ideal teacher is seen as a ‘reflective practitioner’, originally so described by

Schön (1983), who intentionally reflects on and improves his or her own

teaching and learning based on practical experience.

The teacher as a consumer and the teacher as a producer of knowledge

represent two aspects of a teacher’s cognitive skills and attitude towards

knowledge (Gitlin, Barlow, Burbank, Kauchak, & Stevens, 1999; Pendry &

Husbands, 2000; cf. Reis-Jorge, 2005). A teacher should be able to be both a


critical consumer of knowledge, and to build knowledge from practical ex-

perience. These two categories are related to the origin of knowledge that was

discussed in more detail in the previous section about pedagogical know-

ledge. Knowledge was divided into the two subcategories of general and per-

sonal by Morine-Dershimer and Kent (1999) (see also Hiebert et al., 2002).

The focus here is on the stance of a teacher towards all knowledge domains,

including content knowledge, PCK, and pedagogical knowledge. However,

pedagogical knowledge and pedagogical content knowledge, e.g., practicali-

ties and methods used in the classroom, are most likely to be gained through

personal practical experience as well as general theoretical sources. The main

issue is to discuss the cognitive skills that a good (mathematics) teacher

should have in the teaching profession. As D. Cohen (2008) argues, a teacher

should gain a vast knowledge base of various domains related to the teaching

profession, but applying or reformulating knowledge in order to promote the

learner’s processes is another story.

These cognitive skills relate to the research-based approach regarded as a

basis for academic teacher education. However, no agreed view of the sig-

nificance of research-based education or of the benefits of a research ap-

proach exists (Reis-Jorge, 2005). While research-based teacher education

might mean only consuming research-based knowledge about education

(Holligan, 1997; Pendry & Husbands, 2000), over the previous thirty years in

the Finnish teacher education tradition, student teachers have been to gain

competence as critical consumers as well as producers of educational know-

ledge through research activities undertaken during their education (Kosunen

& Mikkola, 2002; Lavonen et al., 2007; Westbury et al., 2005; see also

Brinkman & Van Rens, 1999). The combination of two different approaches,

an academic perspective including formal research procedures and profes-

sional development based on the idea of the reflective practitioner aiming at

on-going self-development is problematic (Reis-Jorge, 2005; see also Bei-

jaard et al., 2004). Similarly, Gitlin et al. (1999) state that teacher educators

should be aware of how student teachers think about research, which could be

introduced to them in a way that would facilitate combining it into their pro-

fessional development.

Consumer of knowledge In academic teacher education, student teachers become acquainted with re-

search findings that they should be able to use for their professional growth

(Gitlin et al., 1999; Pendry & Husbands, 2000). In the study by Gitlin et al.

(1999), both elementary and secondary school teachers regarded educational

research especially as providing methods that can improve teaching in prac-

34 Heidi Krzywacki

tice. Research was seen as helpful for becoming an effective teacher who

knows what works best in the classroom. Holligan (1997) has however ar-

gued that practice in schools cannot be changed through theoretical ideas (see

also Joram, 2007). According to him, students use the ideas that confirm their

previous notions about practice and help them to understand their experi-

ences.

Moreover, student teachers, who are usually practically rather than theo-

retically oriented, find that research literature is written in a way which is

inaccessible to them (Hiebert et al., 2002; D. Cohen, 2008). The role of re-

search and knowledge produced by academics is problematic, even in teacher

education programmes with a strong research-based approach. As a way to

make academic research knowledge more approachable, Gore and Gitlin

(2004) suggest that teachers should be provided with more knowledge and

skills for engaging confidently with research. Gore and Gitlin suggest that the

complexity of research should be discussed, not just introduced as ready and

simplified products during the university courses.

Practical experience, and professional development along with it, seems

to be influential. Gitlin et al. (1999) state that despite the activities provided

and its aims, teacher education has little influence on student teachers’ think-

ing about the fundamental nature of research. However, according to Joram

(2007), the attitudes of teachers toward educational knowledge as a source of

being a good teacher seem to change with teaching experience. In her study,

those who had more teaching experience considered becoming a good teacher

was associated with thinking skills rather with a repertoire of specific teach-

ing skills. D. Cohen (2008) discusses the dilemma of knowledge construction

and valuation of finished knowledge. Teachers should acquire enough know-

ledge about learning and teaching as well as specific content to be able to

support individual learning processes. The more experience they have, the

more accomplished is their knowledge base. However, the finished know-

ledge that they try to offer learners is distant the processes and knowledge

formulation of learners. He takes mathematics as an example of providing

finished knowledge without the procedures required for learners to under-

stand the basics.

It is a challenge to have an influence on classroom performance through

research activities in teacher education. Decision-making is linked with prac-

tical knowledge and experience (Gitlin et al., 1999). Both Carlsen (1999) as

well as Steinberg, Empson, and Carpenter (2004) emphasise the meaning of

the autonomy of a teacher in applying knowledge. On the one hand, an active

role is essential if a teacher is to apply and verify knowledge in each dynamic

teaching situation separately. Outside authority cannot be the basis for mak-


ing decisions. (Carlsen, 1999) On the other hand, providing new instructional

ideas and respecting the autonomous role of a professional is a challenge.

The study by Steinberg et al. (2004) focuses on how teachers are able to use

both practical and research-based knowledge for development of their own

work in the classroom. The aim of the programme was to support teachers in

getting to know children’s mathematical thinking and use it to shift instruc-

tion towards practical inquiry. The potential to adapt the tools for reflecting

on one’s own teaching and the children’s learning was greater when the ideas

were parallel with practical personal knowledge and issues in the classroom

(see also Joram, 2007).

Producer of knowledge The teacher’s stance on knowledge of how to modify and produce the know-

ledge needed in teaching and learning is critical. The research-based ap-

proach is not easy to implement in teacher education in such a way that the

school reality of teaching and learning is taken into account. Kosunen and

Mikkola (2002) claim that the role of research is limited to producing a for-

mal educational thesis during teacher education but the opportunity to inte-

grate smaller-scale inquiry activities with practice does not arise (see also

Westbury et al., 2005).

An inquiry-based approach is one way to promote critical thinking and

on-going learning in work (e.g., Schulz & Mandzuk, 2005; Steinberg et al.,

2004). Schulz and Mandzuk (2005) sum up the recent research showing that

inquiry-based approaches

encourage resistance to thoughtless implementation of teaching practices, support

disposition of critical thoughtfulness about teaching, and nurture the ongoing

learning, professional growth and intellectual development of teacher candidates

(p. 316).

According to Schultz and Mandzuk (2005), students link inquiry with teacher

professionalism, as it is not only associated with classroom practicalities but

also with broader context of the teaching profession. For them, inquiry is

strongly contextualised, and both social and practical inquiry enhance practi-

cal knowledge. However, even if the basic idea of inquiry is internalised,

Schulz and Mandzuk (2005) find it a challenge to address the positional dif-

ferences that teachers experience in school after university.

Research activities have been regarded as one way to educate teachers

who are critical thinkers and skilful in further development in their work.

This necessitates an ability to conceptualise one’s own knowledge and en-

gage with the research approach. In a commentary article, Korthagen (2007)

36 Heidi Krzywacki

lists reasons for the gap between research and practice. A gap between pro-

fessional cultures causes problems in relating research and school practice

with each other. Besides, preconceptions and prior knowledge influence the

way teachers consider research as a part of their work, and furthermore, prac-

tice cannot be understood simply from the cognitive viewpoint, as Atkinson

(2004) states. The last reason for the gap, Korthagen (2007) claims, is the

complexity of teaching. Research-based knowledge cannot be applied di-

rectly and unequivocally, while the notions of practice are various. Forms of

knowledge cause a problem when practical knowledge encounters formal

knowledge (see also D. Cohen, 2008; Hiebert et al., 2002).

A teacher as a reflective practitioner should be able to transform practical

knowledge into professional knowledge in systematic development in his or

her own work. Hiebert et al. (2002) analyse the nature of professional know-

ledge, especially the relationship between practical and formal knowledge

(see also Carlsen, 1999; Reis-Jorge, 2005). Research knowledge is assumed

to be the best basis for professional knowledge because of its generalizable

and objective character. According to Hiebert et al. (2002), practitioner

knowledge has three essential features for a teacher. First, since practitioner

knowledge is linked with practice because it develops in response to practical

problems in the classroom, is grounded in the context, and addresses specific

issues in the classroom. Second, practitioner knowledge is specific, detailed,

and concrete, which might also be seen as problematic. Third, practitioner

knowledge is integrated with and organised by particularities in practice.

Compared with the knowledge of researcher, it is organised according to type

of problem in practice rather than into distinctions among types of know-

ledge. Some additional requirements have to be addressed in transforming

practitioner knowledge into professional knowledge. Hiebert et al. (2002)

emphasise that professional knowledge has to be public, and has to be shared

with others in order to meet such a requirement. Professional knowledge is

then sharable and accumulative. As a last requirement, professional know-

ledge has to be accurate, verifiable, and continually improved.

Student teachers should take an active role in the classroom as profes-

sionals who consume the knowledge acquired in their studies critically and

produce knowledge through practical experience. In particular, because of the

structure of Finnish teacher education, students should integrate different

knowledge areas into a coherent personal knowledge base and improve cog-

nitive competence later in their teaching careers. From the viewpoint of

teacher identity formation, skills in consuming and producing professional

knowledge are embedded in the student’s awareness not only of separate

knowledge domains but also of the way to combine such skills with profes-


sional development and classroom activities (e.g., Beijaard et al., 2004;

Smith, 2007). For example, teachers produce different kinds of knowledge of

teaching and learning in the classroom, e.g., knowledge about pupils through

formal and informal evaluation. Altogether, despite the origin of knowledge,

the ideal in the Finnish educational system is that the teacher is able to use

knowledge in decision-making, e.g., in classroom implementation as well as

curriculum work. Furthermore, the ability to develop further in the teaching

profession is based on thinking skills, and the ability to consume and produce

different kinds of knowledge (e.g., Kosunen & Mikkola, 2002).

3.2 Affective aspects

The cognitive perspective associated with becoming and being a professional

mathematics teacher is only one way to research identity formation (Beijaard

et al., 2004). Emotions and subjectivity play an essential role in teaching and

learning. Recent educational research has emphasised the role of the emo-

tions intertwined with all aspects of teaching and learning (e.g., Beijaard et

al., 2007; Hargreaves, 1998; Korthagen, 2007; Schutz & Lanehart, 2002).

Learning is not a straightforward process that can be directed simply by its

cognitive aspects (Boekaerts, 1999). The affective aspects, especially those

associated with being a teacher are discussed here in particular relation to

teacher identity. First, notions of the ‘human factor’ (after Korthagen, 2007)

in teaching, including affective aspects of teaching and learning in general,

are of interest. Affective aspects of teacher professional identity are discussed

after the overview.

The meaning of emotions and willingness has been brought up in trying

to promote teacher change (e.g., Boekaerts, 1999; Hargreaves, 1998). Teach-

ers do not act simply according to logic or in a predictable way. Korthagen

(2007, p.305) underlines the ‘human factor’ perspective because the cognitive

stance is insufficient to understand teaching practice. Personal emotional re-

actions are part of being a teacher and, in his words, ‘humans do not act on

the basis of logic alone, and from an actor-perspective there are often signifi-

cant personal reasons for not acting such a manner’. Likewise, Hargreaves

(1998) stresses that being a good teacher takes more than just mastering the

school subject and being effective. In his study, the emotional perspective is

embedded in the political environment of educational reform. Emotional rela-

tionships with students are of special interest, and Hargreaves (1998, p. 835)

describes teachers as ‘emotional, passionate beings who connect with their

students and fill their work and their classes with pleasure, creativity, chal-

38 Heidi Krzywacki

lenge, and joy’. The emotional reactions of teachers, such as lack of willing-

ness, have dragged on desired changes directed by policy-makers (Boekaerts,

1999).

The ‘human factor’ of the teaching profession can also be approached

through characteristics associated with the quality of a teacher. Fajet et al.

(2005) use the concept of the ‘affective qualities’ of a teacher, originally

introduced by Weinstein (1989), alongside the cognitive category. In this

category, they include personal characteristics by which the quality of a

teacher, either good or bad, can be profiled, including confidence, inter-

personal skills, and commitment. Similar to Younger, Brindley, Pedder, and

Hagger (2004), Fajet et al. (2005) state that it is not only about particular at-

tributes but also moralistic constructions and visions associated with being a

good teacher. Affective qualities include personal characteristics, attitudes,

and behaviour towards students as well as attitudes towards teaching in gen-

eral.

The personal perspective, including a variety of affective aspects, also

appears in research on teacher identity (e.g., Atkinson, 2004; Walkington,

2005). Eteläpelto and Vähäsantanen (2006) state that various competences

are integrated into personal professionality through subjective meaning-

making (see also Beijaard et al., 2004; Danielewicz, 2001). They highlight a

need for the personal approach alongside the social construction of teacher

identity, especially because of emotional reactions related to personal experi-

ences throughout the process. Hodgen and Askew (2007) discuss the special

role of mathematics in teacher identity. Since mathematics generates strong

reactions, a need for attitude change exists. Teacher identity and emotion are

connected in three ways according to Hodgen and Askew (2007):

(1) Emotions are connected to the figured aspects of identity and to imagination

and desire. Desire for an unattainable completeness is linked to identity.

(2) The relationship between knowledge and emotions, the importance of personal

relationship with mathematics being essential. This idea is founded on DeBellis

and Goldin’s (2006) analysis of knowledge and emotions. Associated with this,

intimacy means a kind of vulnerability of one’s identity.

(3) Emotions of positional identity relate to the development process and one’s

experiences. (pp. 474–475)

Alongside personal experiences, engagement in the teaching profession and

values are part of subjectivity. Knowles (1992) uses the concept of ‘strength

of teacher role identity’ in the sense of how strongly student teachers engage

in the teaching profession and view themselves as teachers (see also Samuel

& Stephens, 2000). There is a difference between playing a role as a teacher


and truly identifying oneself as a teacher (Danielewicz, 2001; Walkington,

2005). Consequently, an individual has to adopt the teacher identity and to be

able to relate core beliefs to the cognitive aspects of being a teacher (see also

Korthagen, 2004; cf. Beijaard et al., 2000).

Emotions are interconnected with teacher identity at several levels in re-

search, both in the long-term relationship with the teaching profession as well

as feelings that arise during the developmental process (Hannula, 2004;

Hoekstra et al., 2007). In this research, affective aspects associated with the

teaching profession generally are distinguished from situational emotions that

arise during the developmental process of becoming a teacher as well as in

teaching situations. Like the cognitive aspects discussed in previous sections,

the category of affective aspects is one way of profiling the individual state

of teacher identity as well discussing what a good mathematics teacher is like

in general. Taking this as a starting-point, affective aspects of teacher identity

are regarded as ‘traits’ that are understood as something stable and funda-

mental to being a teacher. The category of motivation, discussed by Hannula

(2004), is the basis, representing the subjective perspective. The category of

‘affective aspect’ comprises (1) motivation for and commitment to the teach-

ing profession, (2) values and attitudes toward the profession in general, and

(3) personal characteristics associated with being a teacher, according to the

understanding of Fajet et al. (2005). Especially in the early steps of teacher

identity formation, the questions concerning motivation for becoming a

teacher and the appropriateness of one’s own personal characteristics for the

teaching profession arise.


4 The image of the ideal teacher directing development

The image of the ideal teacher, i.e., what a good teacher is or is not, is seen as

fundamental to the process of individual development (Arnon and Reichel,

2007; cf. Sfard & Prusak, 2005). The image of the ideal teacher is developed

through experiences and influential activities. Students have conceptions of

good teaching and learning in mathematics based on experiences as learners

of mathematics, especially of the ability and skills a mathematics teacher

needs. Conceptions of the ideal teacher can be approached both collectively,

as a socially shared image of a good teacher, and individually as the image

that one has of being a good teacher. Everyone, despite the professional ori-

entation, has their own image of a good or bad teacher at least to some extent.

However, associating this image with teacher identity formation is not self-

evident, even among student teachers (Arnon & Reichel, 2007).

The image of the ideal teacher, however, is approached through three no-

tions. First, I discuss conceptions of a good teacher in general as well as the

background to those conceptions. Second, I examine the image of the ideal

teacher from a collective perspective. The image of the ideal teacher is a so-

cially constructed and shared view of what is seen as essential and valuable in

the teaching profession. Last, I approach the image of the ideal teacher from

the individual perspective. The image of the ideal teacher directs personal

goals that an individual sets. Tension between the present image and the im-

age of the ideal teacher is seen as a force for change (Beijaard et al., 2004; cf.

Sfard & Prusak, 2005; see also Richardson & Placier, 2001). From this point

of view, becoming a teacher is a matter of active direction towards

something; i.e., an individual aspires to be a better teacher in relation to vari-

ous aspects of the profession.

4.1 Conceptions of a good teacher

The educational literature has considered the image of a good or bad teacher

extensively. Fajet et al. (2005) describe the findings of numerous studies on

the image of a good teacher under two categories, the ‘professional compe-

tence’ including mastering certain knowledge and skills, and the ‘affective

qualities’ of a good teacher (see also Arnon & Reichel, 2007). These two

categories relate to the personal characteristics of a good teacher. Arnon and

42 Heidi Krzywacki

Reichel (2007) consider these categories as inter-related, so that they are not

dichotomous but complementary to each other.

In addition, some features of teaching performance are considered essen-

tial to being a good teacher, as in the research by Virta (2002, p. 691), who

found that students described a good teacher as someone who ‘makes the

students think critically, have an enormous capital of information, and is will-

ing to discuss and able to create a positive atmosphere in the classroom’. Re-

lated to classroom activities, classroom management skills and well prepared

and taught lessons are also something related to being a good teacher

(Younger et al., 2004).

Korthagen (2004) wants to broaden the discussion about a good teacher

from the classical dichotomy that emphasises the difference between personal

characteristics and competence as a teacher. While he considers it impossible

to constitute a definite list of the features of a good teacher, various levels of

essential qualities should be examined. Korthagen (2004) proposes a multi-

level model in which levels are within and interconnected to each other. Two

outer levels may be observed by others, (1) the environment, and (2) behav-

iour. A step towards the inner levels is (3) competence related to the teacher’s

behaviour. Korthagen underlines the distinction between the levels of behav-

iour and competence: competencies are conceived as an integrated body of

knowledge, skills and attitudes representing potential for behaviour whereas

behaviour is dependent on circumstances, and the environment in which

competencies are put into practice. Korthagen locates (4) beliefs as the next

level. Interestingly, he distinguishes general beliefs and beliefs about oneself

in the teaching profession. The fifth level is (5) identity that is defined as how

a person sees his or her own (professional) identity. Last, the innermost level

is about (6) mission, the psychological concept of becoming aware of the

meaning of one’s own existence within a larger whole. Korthagen (2004, p.

87) concludes that being a good teacher as well as teacher change takes place

at different levels, stating that ‘teacher’s behaviour, competencies, beliefs,

identity and mission together should form one coherent whole matching the

environment’.

The reasons behind the conceptions of the ideal teacher have been of in-

terest for improving teacher education and its influence. Younger et al.

(2004) as well as Virta (2002) emphasise the significance of one’s own

schooling and memories of particular people who had made a difference (see

also Brown, 2003). Students talked about their own teachers in terms of char-

acteristics and good instruction. Virta (2002) mentions that student teachers

accepted the old-fashion methods of their good teachers and, furthermore,

were missing a strong schema of pupil-centred teaching. However, school

The image of the ideal teacher directing development 43

memories were not the only thing the students mentioned as a reason, finding

that teaching practice placement and especially experienced teachers influ-

ence their views (see also Richardson & Placier, 2001).

4.2 The image of the ideal teacher from a collective perspective

From the collective perspective, the image of the ideal teacher is seen as a

socially constructed view of what is associated with being a good teacher.

According to Sfard and Prusak (2005), both individuals and other people de-

fine what is desirable and worth aspiring to, especially within a particular

community. In other words, ‘designated identity’, the concept used by Sfard

and Prusak (2005), is not always a matter of free choice by an individual but

also reflects socialisation within the context. Consequently, in this research,

the image of the ideal teacher is seen as an interface between individual and

collective perspectives on teacher identity, and thus the element, which can

influence the formation of teacher identity. During teacher education, student

teachers become acquainted with socially shared conceptions of a good

teacher and how to become one. Naturally, as Korthagen (2004) asseverates,

it is impossible to engage with one normative, unanimous description of a

good teacher. However, particular aspects and a common interest as well as

practices associated with teaching profession are socially shared (Gee, 2000).

The formation of teacher identity can be interpreted as socialisation; first,

in the community of teacher education, and, second, in the school context as

a work community (Eteläpelto & Vähäsantanen, 2006; see also Wenger,

1998). The socialisation process has been researched by Walshaw (2004),

who has examined the constitution of teacher identity within teaching prac-

tice. She claims that teaching experiences are not only a place for transform-

ing identity through discourse and interaction but also a place for adopting

norms and organisational teaching procedures (see also Brown, 2003). At the

beginning of a teaching career especially, socialisation with existing norms is

an important influential factor for a novice teacher and a way to become a

‘real’ teacher (Eteläpelto & Vähäsantanen, 2006).

Conceptions of a good teacher and what is seen as worth aspiring to might

differ between an individual and a collective (Archer, 2008; J. Cohen, 2008;

Walkington, 2005). Younger et al. (2004) highlight the challenge of address-

ing possible contradictions and tensions caused by idealism in becoming a

good teacher. Similarly, Walkington (2005) emphasises the meaning of find-

ing mutual understanding regarding the image of being a mathematics teacher

44 Heidi Krzywacki

in order to build trust between teacher educators and students. The core be-

liefs might differ, but mutual respect is the way to address the needs of stu-

dents. According to Walkington (2005), teacher educators should continually

encourage the formation of a teacher identity by facilitating activities that

empower the students to build explicitly upon and challenge their beliefs.

Socially shared aspects of being a teacher also inform collaboration be-

tween teachers. In order to decrease tensions caused by different images of

‘being a good professional’, an individual might position him- or herself in

the community by adopting shared values and seeking success by acting ac-

cording to supposed norms (Archer, 2008). To be recognised by others and to

be treated like a teacher is sought by acting according to certain norms. Ac-

cording to J. Cohen (2008), because individual teachers define and enact

shared aspects of professional identity differently, formal structures to pro-

mote teacher engagement in collaboration with each other are not the same

for all teachers. In her discursive study, teachers try to accomplish significan-

ces of the shared role identity as a teacher through identity talk.

Arnon and Reichel (2007, p. 462) highlight the meaning of breaking the

cycle as ‘if there is no development, growth and change in this primary image

during the teacher education process, students will carry the same images that

they arrived with back to their environments and to their pupils’. Various

interventions based on research are suggested. Korthagen (2004) claims that

it is important to take the concern of students as a starting-point because this

is a driving force for development. In his model, since becoming and being a

teacher is analysed through levels within each other, the types of intervention

that might aid a student varies or has different effects. Besides, principles

provided during teacher education should be embodied in action in order to

have an impact (Danielewicz, 2001). However, even if generalisations about

effective and expert teaching might be useful, these should not be presented

as universal truth (Hagger & McIntyre, 2000). Altogether, if students are re-

garded as having an active role in teacher identity formation, confronting

situations of disagreement and dissonance force them to evaluate and pos-

sibly reshape their views of the ideal mathematics teacher.

4.3 The ideal image orienting individual development

The image of the ideal teacher is meaningful for identity formation when it is

related to personal goals and thus directs personal development (Arnon &

Reichel, 2007; Virta, 2002). The starting-point is that individuals commit

themselves to becoming teachers and are able to identify with the teaching


profession (Danielewicz, 2001). The image of the ideal teacher is shaped in

social interaction with others, e.g., during school time and in teacher educa-

tion. An individual confronts the requirements of society and traditions

through the social conceptions of a good teacher (see J. Cohen, 2008;

Eteläpelto & Vähäsantanen, 2006). However, the image of the ideal teacher

influences the personal developmental process only when it is particularly

associated with this process.

Student teachers, as well as teachers later on in their careers, have concep-

tions of the worthwhile features of the good teacher that they would like to

become. As Korthagen (2007) puts it, prior knowledge and preconceptions

play a powerful role in receiving and learning new knowledge and skills (see

also Hagger & McIntyre, 2000; Knowles 1992; McCormack et al., 2006).

However, the image of the desired state as a teacher is seen to direct the de-

velopmental process through separate aspects associated with the teaching

profession rather than as a coherent entity. A person might have a clear pic-

ture of certain characteristics as a teacher that s/he personally finds valuable

and desirable. The image of the ideal teacher might also be defined through

some undesirable features that a person wants to avoid. Altogether, the image

of the ideal is fragmentarily linked with personal goals through separate as-

pects.

Furthermore, the image of the ideal teacher is seen as dynamic and con-

tinuously in progress. It changes over time in social interaction with others

and with personal experience (Arnon & Reichel, 2007; Danielewicz, 2001).

For example, Arnon and Reichel (2007) have shown that the significance of

knowledge for a teacher changed with teaching experience. Teachers with

professional experience attributed more importance to knowledge than inex-

perienced ones.

An individual has to be aware of his or her own needs in order to be able

to set personal goals embedded in the image of the ideal teacher. It is not

simply about conceptualising the desirable characteristics of a good teacher

but also reflecting one’s present state as a teacher through personal experi-

ence (Danielewicz, 2001). A person has to be able to form the image of self

in the profession in interaction with others. Sfard and Prusak (2005) use the

concept of the ‘designated identity’ of the desired state of being a teacher in

their narrative approach to teacher identity, arguing that designated identities

direct individual actions. Furthermore, they continue that the notion of two

subsets, actual and designated identity, is essential in identity formation. For

them, actual identity is about the existing state of affairs, answering the ques-

tion ‘Who am I as a teacher?’ while designated identity defines the desired

state of affairs, ‘Who do I want to become?’ (see also Beijaard et al., 2004).

46 Heidi Krzywacki

In other words, designated identity is manifested in commitment, desire, or

even obligation to become something different from what is the case at a par-

ticular moment.

To conclude, formation of teacher identity is seen as a process of filling

the gap between two states: existing being as a teacher, which I will call the

present image of teacher identity, and desired state as a teacher, which I will

call the image of the ideal teacher (Beijaard et al., 2004; cf. Sfard & Prusak,

2005). The dynamic nature of teacher identity regarding the internal pro-

cesses of identity formation is embedded in this notion. First, an individual

has to be aware of the present state of his or her own identity at a specific

time and place. Recognition of this is situational, but some aspects remain

more stable than others. The question is about traits that constitute an under-

standing of one’s state and potential as a teacher. Second, a person should

become aware of the image of the ideal teacher underpinning personal devel-

opmental goals. Similarly, the ideal image as well as personal goals are dy-

namic and momentary but recognisable at certain times and places. The ten-

sion between the present and desired state of identity is a driving force for the

on-going and dynamic process of identity formation. According to Sfard and

Prusak (2005), an individual decreases this tension through learning (see also

Wenger, 1998; Bohl & van Zoest, 2002).

It is a challenge for students to reflect on their own state as a teacher as

well as to set personal goals on the basis of the image of the ideal teacher.

Virta (2002) found connections between the image of what she called a good

teacher and the goals that students set for their own development among a

group of student teachers (see also Arnon & Reichel, 2007). Both Virta

(2002) and Younger et al. (2004) have shown that students highlight the sig-

nificance of personal characteristics in evaluating their individual strengths

and developmental needs. Almost surprisingly, limited content knowledge as

a specific knowledge domain was of concern rather than teaching skills.

However, discussion on the significance of the ideal teacher is not automati-

cally connected to the concept of teacher identity or self-regulated learning.

For example, Arnon and Reichel (2007) state that

the actual discussion of the image of the good teacher during teacher education is

a method of raising consciousness and stimulating thought processes, enriching

the image of the ideal and turning the theoretical discussion into an instrument of

the process of preparing the student of education (p. 261).

For them, examination of the images of the ideal represented by students is a

way to evaluate the effectiveness of the teacher education programme.


In this research, the concept of the ‘present image of teacher identity’

stands for understanding of an existing state as a teacher, in this case under-

standing emerging professionalism as well. The main idea is in accordance

with the notion of actual identity used by Sfard and Prusak (2005), but the

wording ‘present’ describes better the notion of something that takes place as

a part of teacher identity formation from the individual perspective. The indi-

vidual can reflect on his/her state as a teacher, according to Beijaard et al.

(2004), based on interpretation of personal experience (How am I as a

teacher?), whereas others use observations, for example, in classroom situa-

tions (How is an individual as a teacher?) to build up their understanding of

an individual as the basis for influential social interaction. The image of the

ideal teacher includes the view of what a good mathematics teacher is in

general, collectively and individually (after Arnon & Reichel, 2007). Both

images are regarded as dynamic and continuously progressive entities. Be-

sides, such images can be described through separate characteristics related to

the teaching profession, e.g., through knowledge and skills as well as the af-

fective aspects associated with being a teacher.

However, the assumption is that the image of the ideal teacher directs per-

sonal development depending on how strongly the ideal image is linked to

the personal goals that an individual sets, i.e., what kind of teacher would I

like to become? According to Arnon and Reichel (2007), personal goals are

in accordance with the image of the ideal teacher but do not necessarily cover

the ideal image in all respects. Consequently, personal goals do not necessa-

rily constitute a complete picture of the ideal teacher that a person identifies

with. The image of the ideal teacher is more like a combination of desirable

features than a coherent embodiment of the ideal teacher. Therefore, the con-

cept ‘designated identity’ used by Sfard and Prusak (2005), despite the com-

mon idea behind the notion, is not used here: firstly, the image of the ideal

teacher is not seen as an overall desired state, and, secondly, it does not ne-

cessarily direct development. Furthermore, both notions, the present image

and the image of the ideal teacher, are equally ‘actual’ for the person in-

volved with the process.


5 Teacher identity as an on-going process

Professional identity is seen as constructed and continuously reshaped by the

individual in interaction with others (Beijaard et al., 2004; Coldron & Smith,

1999; Danielewicz, 2001; see also Jenkins, 2004). Here, the model intro-

duced by Côté and Levine (2002) is considered as a starting-point for de-

scribing the on-going process of the formation of emerging teacher identity in

more detail (Figure 2). As in the model, processes are divided into two cate-

gories, internal and external, through which the mechanisms of teacher iden-

tity formation can be analysed.

Figure 2. Teacher identity formation as an on-going process (Côté & Levine, 2002,

p.134)

The relationship between personal and ego identity components represents

internal processes of teacher identity formation. At the level of personal iden-

tity, an individual engages in interaction with others within a given context.

First, the outcome of that influential interaction is internalised by an individ-

ual depending on meaningfulness and individual needs. In the case of teacher

identity formation, a person has experiences with others, which influence the

image of the ideal teacher and general perceptions of the teaching profession

(see also Arnon & Reichel, 2007). However, a person internalises only some

socially shared ideas related to the teaching profession as a part of a personal

image of the ideal teacher. A person filters influential ideas and constructs

own understanding of being a teacher in general as well as perceptions of

Social identity (social structure)

Ego identity (personality)

context

person

Personal identity (interaction)

3

4 EXTERNAL

INTERNAL 2

1

50 Heidi Krzywacki

oneself as a teacher. Second, a person not only internalises the outcome of

interaction but also constructs an understanding of him- or herself as a

teacher in accordance with previous internalisations and inner understanding.

Previous experiences through which an understanding has developed are im-

portant to the internal process (Nelson, 2008). In particular, teacher identity

includes the idea of ‘feeling as a teacher’; i.e., since a person engages with

the idea of self as a teacher, taking a role as a teacher and a real internalised

teacher identity are distinguished from each other. A person thus has an ac-

tive and fundamental role in teacher identity formation, especially at the be-

ginning of identity formation during teacher education.

The interaction between personal and social components represents the

external processes of teacher identity formation. A person has contacts with

other people in everyday life, an interaction through which individuals con-

struct social reality and become aware of socially shared perceptions. In the

case of teacher identity formation, socially shared ideas of the teaching pro-

fession and especially being a good teacher, i.e., the image of the ideal

teacher, are essential for identity formation (e.g., Sfard & Prusak, 2005). Tra-

ditions, educational culture, and a socially accepted way of action represent

those shared ideas implemented and reproduced by people. Teacher educa-

tion is one of the institutions that intermediate socially shared ideas of being

a good teacher and that socialises student teachers with existing values and

norms. However, opportunities to participate in construction of shared under-

standing of the teaching profession are limited during teacher education. In

this research, external processes of teacher identity formation and the rela-

tionship between personal and social identity levels are not the main concern.

However, one cannot examine identity formation without considering the

meaning of social interaction and the context in which a person acts.

The on-going process of teacher identity formation includes the idea of

change and development. Richardson and Placier (2001) summarise the na-

ture of change by invoking four themes. First, they discuss how change is

defined and by whom. Since teacher identity formation always involves a

person (Beijaard et al., 2004), it is a subjective understanding of the forma-

tion process and possible changes in it. However, the idea of engagement in

interaction with others and external processes of identity formation includes

the idea that the process is sharable and can be partly recognised by others

(Gee, 2000). Others such as teacher educators and peers can then also define

the change. In this research, the change is defined in terms of development in

cognitive and affective aspects of the teaching profession understood through

both present and ideal images.

Teacher identity as an on-going process 51

Second, the question of who has the power over change is crucial. In the

case of teacher identity formation, even within teacher education, this is the

students themselves. Of course, structural and cultural constraints as well as

the established path for developmental direction influence the process of

change as well. However, the students’ role is collaborative and they make

their own decisions regarding the personal process of emerging teacher iden-

tity they are involved in.

Third, the change entails the idea of direction towards something. Here,

the image of the ideal teacher directs the change, since ‘becoming a good

teacher’, can be regarded as an obvious aim of developmental process. How-

ever, the definition of a good teacher and aspects such as knowledge and

skills needed as a teacher differ between persons.

Last, Richardson and Placier (2001) discuss difficulties in describing or

identifying general stages of development. In general, the theoretical frame-

work is based on Côté and Levine’s social psychological model (2002). Iden-

tity formation is seen as a continuous process involving both internal and

external factors. From the individual perspective, the tension between the

image of the ideal teacher and the present image of oneself as a teacher is a

driving force for change. However, the basic assumptions about the individ-

ual active role and individual trajectories entail the idea that it is not possible

to find developmental stages in teacher identity formation. The individual is

the one who determines which experiences have an influence on individual

development and how (Danielewicz, 2001; Sfard & Prusak, 2005; Wenger,

1998).

5.1 Internal processes of identity formation

According to Côté and Levine (2002), a person constructs an individual view

of reality through internal processes and, in the case of teacher identity, a

person constructs an understanding of becoming and being a teacher the same

way. Internal processes are bidirectional. On the one hand, a person filters

and internalises an influential outcome of interaction with others on the

grounds of one’s own needs, liking, core beliefs, and personal tendency

(Walkington, 2005). Personal motives and student background pave the way

for the internalisation process. Hodgen and Askew (2007) discuss the will-

ingness to aspire for development as a teacher. In addition to the internalisa-

tion of external impacts, the aim of teacher identity formation is that one

comes to ‘feel that s/he is a teacher’ and identify oneself with being a teacher,

distinguishing between a role as a teacher and professional identity. On the

52 Heidi Krzywacki

other hand, a person constructs a self-presentation based on previous internal-

isations (after Côté & Levine, 2002), which is a suitable impression for others

to recognise at the level of personal identity. A person constructs a personal

understanding of being a teacher through lived experiences within a particu-

lar context.

Notions associated with teacher identity formation from the personal per-

spective will now be discussed. First, a person’s background, including mo-

tives for and commitment to the teaching profession, are seen as essential to

the process. Since the research is about the early steps in identity formation

during pre-service teacher education, it emphasises the student teacher’s

viewpoint. Second, the notion of ‘becoming a teacher’ is elaborated in more

detail, since a person should be able to identify with being a teacher. Last,

identity formation takes place through experiences with others, since differ-

ent experiences are a core element in teacher identity formation, which a per-

son undergoes in interaction.

5.1.1 Student teacher background

The student teachers’ background embedded in both professional and per-

sonal life experiences is meaningful for the process of becoming a teacher,

for the formation of teacher identity (Beijaard et al., 2000; Richardson &

Placier, 2001). What an individual brings has an influence on conceptions of

teaching and learning generally, the image of being a teacher, and the student

teachers’ motivation including motives for applying for the teacher education

programme (e.g., Haritos, 2004; Merenluoto, 2003; Virta, 2002; Younger et

al., 2004).

The reasons for becoming a teacher are many and, despite national differ-

ences, common themes can be seen internationally (Virta, 2002). One of the

reasons for becoming a teacher and entering the programme is the value of

the school subject itself. For those students, becoming a teacher means an

opportunity to continue working within a subject area, like mathematics. The

other reason is one’s own school experiences or encouraging teaching experi-

ences in school as an unqualified teacher. However, according to Virta

(2002), the influence is not clear as some students give positive experiences

as a reason, but others express critical attitudes towards their schooling be-

cause of frustration or negative experiences. Passion and emotional commit-

ment to teaching, beside the desire to work with children, are also mentioned

as reasons for embarking on a teaching career, according to Younger et al.

(2004). Moreover, a majority of students see teaching as an opportunity to


make a difference (O’Brien & Schillaci, 2002). However, not all students are

so noble; pragmatism is a key factor for those who claim that being a teacher

is a meal-ticket (Richardson & Watt, 2005). Secondary student teachers

might also view teaching as a stepping-stone to other careers. Besides, it is

also a second choice for those who are not so successful in subject matter

studies. (O’ Brien & Schillaci, 2002) In all, the orientation towards teacher

education differs among student teachers.

Student teachers have two kinds of role in learning to teach in the teacher

education programme. Firstly, they are becoming teachers for schools in the

future and one’s image as a teacher is a central aspect of professional devel-

opment (Malmberg, 2006). Secondly, student teachers are also learners

guided by teacher educators. They have a particular orientation toward uni-

versity course and experience the learning process as a student. The nature of

motivation influences the way students study and learn in university studies

(Nolen, 1996). In Finnish research on study orientations of university stu-

dents, Mäkinen and Olkinuora (2004) noted that four groups differed from

each other regarding general study orientations, applied learning strategies,

and study success: performance-orientated, task orientated, socially-

orientated students and avoiders. A need for study guidance is essential ac-

cording to Rautopuro and Väisänen (2002), as students who are committed to

studying and are aware of their motives achieve both more success and satis-

faction. In the mathematical field, the general study orientation of students

seems to vary greatly (Mäkinen & Olkinuora, 2002). They continue that one

reason for avoiders is instrumental motives for studies; many students in

mathematics and physics for example attend university studies as they want

to improve their knowledge base in order to apply to medical school or tech-

nical studies (see also Virta, 2002; cf. Merenluoto, 2003).

The way student teachers engage in becoming a teacher, i.e., developing

themselves as teachers, is essential for the formation of teacher identity (Bei-

jaard et al., 2004; Danielewicz, 2001; Malmberg, 2006). Construction of a

new professional identity is a challenging process, in which an individual

confronts the need to question his or her own pre-conceptions (Kagan, 1992;

Trotman & Kerr, 2001; Fajet et al., 2005). Students should be able to imagine

themselves as teachers and think about their own preconceptions and atti-

tudes related to teaching and learning (see also Bohl & van Zoest, 2002).

Furthermore, students should set personal goals in order to orient to individ-

ual development. Danielewicz (2001) highlights that there is not only one but

many ways to develop identity. Since individual work on teacher identity

formation is needed to make progress, supporting individual identity forma-

tion is a challenge because of different needs and backgrounds.

54 Heidi Krzywacki

Younger et al. (2004) have divided student teachers’ expectations of their

studies into three sub-categories. First, learning in university courses is one

way to learn to teach, especially a way to learn the content knowledge needed

as a teacher. Second, the opportunity to observe experienced teachers in

classroom contexts is also a way to learn as a teacher. Students need to have a

model to identify with and to be able to see ideas of teaching and learning in

practice (see also Haritos, 2004; Trotman & Kerr, 2001). The last category,

unsurprisingly, was learning through doing. It is not only about an oppor-

tunity to take a role as teacher but also getting feedback from experienced

teachers. At the same time, there are also findings that student teachers seem

to assign great importance to their personal characteristics and less import-

ance to education. Fajet et al. (2005) state that pre-service teachers consider

teaching primarily as a task involving affective, interpersonal relationships

rather than a profession requiring a skilled and knowledgeable practitioner

(cf. Virta, 2002).

5.1.2 Becoming a teacher

The question of how teacher identity exists and especially what it means that

an individual student teacher grows to be a teacher needs to be discussed. As

mentioned before, research on (teacher) identity varies greatly and, conse-

quently, the understanding of ‘becoming and being a teacher’ differs. Some

research distinguishes a professional self from a personal self on the grounds

of intrapsychological processes, so that ‘becoming a teacher’ means a change

in inner understanding (Korthagen, 2004). Some regard teacher identity as

consisting of several sub-identities (Beijaard et al., 2004), while others regard

identity as a unity that develops and appears differently at different times and

places (Sfard & Prusak, 2005). The point of departure of this research is the

model based on the three components of identity: ego, personal and social

identity (Côté & Levine, 2002) and, according to the model, teacher identity

coexists at all three levels. It is not possible to found teacher identity on only

one of these three, even though it can be approached from each separately.

Since this research focuses on the early steps of emerging teacher identity

during pre-service teacher education, ‘becoming a teacher’ is of special inter-

est from the perspective of the person and internal processes.

In the model presented by Côté and Levine (2002), the focus is on the ego

identity level, which involves internal processes not directly visible to others.

Eteläpelto and Vähäsantanen (2006) highlight the significance of perceptions

of oneself, one’s own role and commitment to the teaching profession for


teacher identity. Similarly, Beijaard et al. (2000) have investigated teacher

identity through individual perceptions of professionality and especially from

the perspective of teacher knowledge domains. ‘Becoming a teacher’ means

growing to be a teacher, i.e., how comprehensively one identifies oneself

with being a teacher.

Moreover, there is a difference between acting as a teacher and being a

teacher, i.e., genuinely adopting teacher identity (Danielewicz, 2001). The

way teacher identity is recognised by oneself and others makes the difference

(Gee, 2000). A person is only taking a role if s/he gives the impression of

being a teacher, e.g., performing like a teacher in the classroom and school

environment but, despite the real image that others recognise, not regarding

him/herself as a real teacher. Walkington (2005) states, based on Mayer

(1999), that

a teaching role encapsulates the things the teacher does in performing the func-

tions required of her/him as a teacher, whereas teaching identity is a more per-

sonal thing and indicates how one identifies with being a teacher and how one

feels as a teacher (p. 54).

When merely taking a role as a teacher, others recognise a person as a teacher

based on self-presentation that takes place at the personal identity level and

indirectly at the social identity level (after Côté & Levine, 2002). However, at

the ego identity level, being a teacher is not internalised by a person when

taking a role.

The process of becoming a teacher is closely involved with interaction

with others. According to research by Wenger (1998) and some based on

Wenger’s ideas (e.g., Bohl & van Zoest, 2002; Hodgen & Askew, 2007;

Swennen, Volman, & van Essen, 2008), identity formation is seen as a result

of learning within certain communities of practice. For example, Bohl and

van Zoest (2002, p. 139) claim that ‘our identities exist not only within our-

selves, but are also strung across a continuum between ourselves and others’.

Similarly, Samuel and Stephens (2000) discuss teacher role and identity from

both the perspectives of the individual and the cultural environment. Com-

pared with the model of Côté and Levine (2002), the focus is then on the ego

and personal identity levels, at which self-presentation takes place. ‘Becom-

ing a teacher’ has also been associated with having a position in the school

community. McCormack et al. (2006) regard teacher identity as connected

with position and recognition by others (see also Gee, 2000).

Social theories have been criticised for failing to deal with the subjectivity

and internal processes that teacher identity development involves (e.g.,

Eteläpelto & Vähäsantanen, 2006). Volman and ten Dam (2007) claim that an

56 Heidi Krzywacki

individual is someone who has a dominant role in interplay between social

and individual perspectives, maintaining that social identities structure the

learning processes that a person engages with. However, the image of self,

perceptions of oneself as a teacher in this case, directs individual commit-

ment and what is seen as worth aspiring to. Similarly, Côté and Levine

(2002) talk about an individual who filters external influences in the continu-

ous process. Because of the active role in directing and filtering influential

interaction, an individual him/herself has to be motivated to become some-

thing and develop him/herself through learning (see also Danielewicz, 2001).

‘Becoming a teacher’ is associated with the idea that an individual grows

up in some way and changes at the ego identity level (after Côté & Levine,

2002; see also Richardson & Placier, 2001). Promoting this change through

new knowledge and skills provided in the pre-service teacher education

courses is a challenge. Student teachers bring influential, distinctive percep-

tions about teaching and learning to teacher education, and this variety should

be taken into consideration somehow (Hagger & McIntyre, 2000; Kagan,

1992). Smith (2007) discusses the need to consider what different knowledge

areas, like mathematics, mean to professional identity. Subject matter studies

influence the views of teaching and learning that student teachers have (see,

e.g., Foss and Kleinsasser, 1996). Since the way of thinking in mathematical

and natural sciences as disciplines is different from that in educational sci-

ences, student teachers might have difficulty in understanding the idea of

educational studies and pedagogical knowledge after studying for many years

in a subject department (Brinkman & Van Rens, 1999; cf. Joram, 2007). In

addition to subject matter studies, student teachers should become acquainted

with educational research as a part of being a professional teacher (Gitlin et

al., 1999; Gore & Gitlin, 2004; Reis-Jorge, 2005).

The question concerns not only what is seen as valuable knowledge and

skills, but also how student teachers learn new things and change. Pre-service

teachers tend to use their personal experiences as critical filters in adopting

and integrating new content into their professionality (Malmberg, 2006; see

also Volman & ten Dam, 2007). Student teachers should be able to reflect

upon their own preconceptions of pedagogical knowledge and should under-

stand the meaning of the key concepts used in designing, organising, and

evaluating learning and instruction (Haritos, 2004; Younger et al., 2004; see

also Da Ponte, Oliveira, & Varandas, 2002). Trotman and Kerr (2001) claim

that two stages can be addressed through integrative activities. Firstly, stu-

dent teachers become conscious of the values and beliefs that they have in-

ternalised as a consequence of previous activities and experiences (see also

Foss and Kleinsasser, 1996; Kagan, 1992). Secondly, beside becoming aware


of their own background, students should be given opportunities to reflect

critically on and expand the understanding they derive from making the in-

ternal more external and explicitly understood. This may make the students’

sense of themselves as a teacher richer, so that the desired transformation of

perspective is easier to achieve (see also Danielewicz, 2001). However, as

Trotman and Kerr (2001) and Senger (1999) state, changes in thinking do not

necessarily lead to changes in action, here understood as a change at the per-

sonal identity level in Côté and Levine’s model (2002). Promoting real trans-

formation is a challenging task.

In this research, ‘becoming a teacher’ is associated with the process of

change. As discussed in the previous section on the image of the ideal

teacher, one’s awareness of the present state of emerging teacher identity as

well as awareness of the personal aims in relation to the image of the ideal

teacher is fundamental to this process. In Côté and Levine’s model (2002),

‘becoming a teacher’ takes place primarily at two levels, ego and personal

identity. The state of teacher identity is to be recognised both individually

and socially. Even though teacher identity is socially constructed in interac-

tion with others and is recognised as situated and shared by others, an indi-

vidual has a fundamental role in directing the change and in giving meaning

to experiences. In other words, teacher identity cannot be discussed without

considering the understanding of the individual, the one who ‘feels’ like a

teacher and whose face is recognised by others. In academic teacher educa-

tion, integrating new knowledge into professionality is important for the pro-

cess of ‘becoming a teacher’, i.e., learning and strengthening competence as a

teacher is one way to grow to be an autonomous teacher. ‘Becoming a

teacher’ means gradual changes in an individual through both adaption and

through adopting something based on social influences. For changes to take

place, a person needs confirmation and to be seen as a teacher in interaction

at the personal identity level within the context.

5.1.3 Teacher identity constructed through experience

Experiences are essential to teacher identity formation (Beijaard et al., 2004;

Nelson, 2008; Samuel & Stephens, 2000). In Côté and Levine’s model

(2002), the boundaries between a person and context are at the personal iden-

tity level, where others perceive the individual state of identity through self-

presentation. The actions that a person engages in in everyday life are the

basis for individual experience. However, the meaning of events depends on

the person and his/her previous internalisations at the ego identity level. As

58 Heidi Krzywacki

Sfard and Prusak (2005) explain, our vision of our and others’ experiences is

essential for constituting identities, not experience as such.

For the individual, experiences form a continuum between past and future

mediated by present experiences. In the Deweyan way of understanding ex-

perience, continuity is seen as a fundamental feature of experience (Nelson,

2008). A person intertwines previous and present experiences with each

other. Dewey’s understanding of experience (1938) is as a moving force

grounded in situation, rooted in interaction, and related to the individual’s

life. First, experiences are always situated in a certain time and place, mean-

ing that they cannot be separated from the context and time in which they

occur. Second, interaction plays a central role for experience to occur at a

particular time and place. Third, experience cannot be separated from the

person having it. Experiences are always in continuity with personal life and

actually defined as of a particular kind by the person concerned (Nelson,

2008). For Sfard and Prusak (2005), identity talk is seen as a tool for copying

with new situations in terms of past experiences and becoming able to plan

for the future in their narrative approach.

In terms of Côté and Levine’s multidimensional model (2002), past ex-

periences are encapsulated in previous internalisations at the ego identity

level and have an impact in identity formation through the inner processes of

the person him/herself (Knowles, 1992). Samuel and Stephens (2000) associ-

ate experiences with professional identity, especially the image as a teacher

arguing that not only questions about the present state and future designated

image as a teacher should be addressed, but the past always brought by the

individual should also be taken into consideration. In other words, the phe-

nomenon should be examined based on three questions: Who am I? (present),

What do I wish to become? (future), and What do I bring with me? (past).

‘Becoming a teacher’ means a change towards something. For example,

Da Ponte et al. (2002) state that professional knowledge is not enough with-

out internalising and adopting new ideas as a part of personal views and, in

order to promote changes, reflection upon experiences is needed to stimulate

thinking. Through experiences, a person gains new knowledge about teaching

and learning. Kagan (1992) states that student teachers need to experience

what works and why it works in the classroom as they engage in technical

rationality. Similarly, Gore and Gitlin (2004) have noted that teachers choose

to rely on the experiences of trusted colleagues as a basis of knowledge in-

stead of research knowledge produced by academics.

Active reflection on experience should take place to promote develop-

ment as a teacher. Students have traditionally been directed to reflect on their

cognitive processes in academic teacher education. Morine-Dershimer and


Kent (1999) underline the meaning of reflection in promoting the interplay

between general and personal pedagogical knowledge. While personal know-

ledge formed by practical experiences is broadened and made more objective,

conceptions and principles of pedagogy explicated by research are contex-

tualised. Some research distinguishes reflectivity and reflexivity from each

other. Danielewicz (2001) considers reflexivity as the act of self-conscious

consideration that is an instrumental and intentional means to an end,

whereas reflection is directed towards something that has already happened

(see also Côté & Levine, 2002). Walkington (2005) finds it challenging for

teacher educators to mentor student teachers toward reflective activities in-

stead of supervising performance as a teacher, functional competence in the

classroom.

Experiences are also important for the affective aspects of teacher identity

formation (Walkington, 2005). Atkinson (2004) criticises the view that

stresses the cognitive viewpoints of becoming and being a teacher. He under-

lines the role of non-rational aspects in understanding the meaning of experi-

ences, and through that, their influence on the formation of professional iden-

tity. An individual needs to construct fantasy through narratives, which al-

lows understanding of all aspects of experience in a meaningful way. In fact,

Atkinson states that formation of teacher identity is not only about reflective

actions on practical experiences, which are based on rationality and thinking

skills. He claims that reality is constructed partly in imagination, through

which the notions of reality are completed and made meaningful for an indi-

vidual (see also Sfard & Prusak, 2005).

Emotions that an individual experiences in different situations are particu-

larly bound up with identity formation (Schutz & DeCuir, 2002; see also

Hannula, 2004). When a person engages in interaction at the personal identity

level, emotions and feelings play an important role in various situations. A

subjective stance towards becoming and being a teacher subsists. Korthagen

(2007, p. 305) states that ‘the problem of promoting fundamental professional

change is first of all a problem of dealing with natural emotional reactions of

human beings to the threat of losing certainty, predictability, or stability’.

Similarly, Danielewicz (2001) notes the need for students to build confidence

and have a feeling of efficacy and empowerment. Hodgen and Askew (2007)

associate emotions with teacher identity formation through positioning in a

particular context. Emotions are seen as a way for a person to find out who

they are, what they value, and what matters in specific classroom contexts

where identity is reshaped (after Op ’t Eynde, De Corte, & Verschaffel,

2006). Although a person can recognise his or her own state regarding feel-

ings as a teacher, it is problematic to build it externally in interaction. As

60 Heidi Krzywacki

Korthagen (2007) asserts, human change can take many forms (see also Nel-

son, 2008). Besides, longer-lasting change is not necessarily as expected or

immediately visible to others or the individual him/herself.

Côté and Levine (2002) claim that previous experiences and internalisa-

tions influence the self-presentation that a person provides to others (see also

Beijaard et al., 2004). In other words, when an individual engages in interac-

tion with others at the personal identity level, s/he relies on previous experi-

ences and understanding in defining situations and reshaping the performance

visible to others. All students have plenty of life experience before entering

teacher education and making a decision about a future professional career.

Once committed to the process of becoming a teacher, a person interprets

past experiences in a new way and possibly associates them with the future

profession. In the case of mathematics student teachers, mathematics as a

discipline and mathematical learning experiences have a strong influence on

emerging professional identity. Hodgen and Askew (2007) highlight math-

ematical intimacy and mathematical integrity (after DeBellis & Goldin, 2006)

as essential for learning in terms of identity construction. DeBellis and

Goldin (2006, pp. 137–138) define mathematical integrity as the ‘individual’s

affective psychological posture in relation to when mathematics is ‘right,’

when a problem solution is satisfactory, when the learner’s understanding

suffices, or when mathematical achievement deserves respect or commenda-

tion’. By mathematical intimacy, they mean deeply-rooted emotional en-

gagement, vulnerability and the building of mathematical meaning and pur-

pose for the learner. These aspects of the teacher’s own previous learning

process in mathematics influence identity formation.

Students start to see themselves differently with teaching experience in

the classroom. They begin to notice the differences between the image of the

ideal teacher and their present state as a teacher (Arnon & Reichel, 2007).

Students traditionally expect that teaching experience will teach how to teach

(Grossman, 1990). For identity formation, it is essential that one has the op-

portunity to experience oneself as a teacher and build up an understanding of

oneself as a teacher based on feedback, and to face uncertainty and self-doubt

(Settlage et al., 2009; Burn, 2007). Côté and Levine (2002) discuss the con-

scious impression conveyed to others and the constructed self-presentation

through which a person engages in interaction. In teacher education, teaching

practice provides an opportunity for social interaction and engagement in the

school context (Walshaw, 2004).


5.2 External processes of identity formation

Since the process of teacher identity formation is situated and embedded in

social interaction, an overview of the framework of social perspective needs

to be included here; e.g., discussing the meaning of social interaction and the

context in which a person acts (Bohl & van Zoest, 2002; Eteläpelto &

Vähäsantanen, 2006). The purpose is not to cover the social perspective com-

prehensively but to frame the aspects that allow talk about teacher identity as

a situated and shared phenomenon. Some particular themes regarding identity

formation that emerge during the early steps of the formation process are

discussed.

Côté and Levine’s model (2002) was introduced earlier in this chapter.

External processes operate when a person engages in interaction with others

in a specific context. Côté and Levine (2002) talk about the interplay between

the levels of personal and social identity components that involve others be-

side the individual. In practice, a person interacts with others and participates

in communication through everyday life. While individuals build their social

understanding of what it means to be a teacher by constructing social reality

collectively and possibly challenging the existing constructions (Côté & Lev-

ine, 2002), an individual becomes aware of the existing social understanding

of what it means to be and become a teacher through traditions and shared

understanding of being a good teacher in a particular community.

Teacher education represents an institution that intermediates these so-

cially shared ideas and through which student teachers become involved in

socialisation processes. The aim of teacher education is to support the process

whereby students become professional teachers, or at least construct a basis

for professional development later in work. From the perspective of external

processes, a person uncovers his or her state as a teacher through self-

presentation and thus makes the individual state of identity recognisable to

others at a particular time and place (Gee, 2000). Danielewicz (2001) calls

this going public. Other people recognise the state of identity not only on the

basis of physical characteristics but in reference to the context. An individual

self defines the state of teacher identity through feedback and experiences in

different situations, including comparisons with others (see also Beijaard et

al., 2004).

This research discusses the aspects associated with social understanding

of teacher identity utilizing three themes that emerge from the literature re-

view. Firstly, a brief discussion of identity as a socially constructed entity is

given. Identity formation is then seen to take place through learning and

shared experiences (e.g., Wenger, 1998; Volman & ten Dam, 2007).

62 Heidi Krzywacki

Wenger’s theory about learning and communities of practice (1998) is intro-

duced because it is widely used in research on mathematics education. Sec-

ondly, teacher identity is seen as a situated phenomenon that exists in relation

to contextual aspects, like traditions in the school environment. It is note-

worthy that these two themes are neither fully satisfactory nor exclusive but

rather provide one way to consider the social perspective of teacher identity.

These aspects interact – one cannot examine contextual aspects, like the

community in which individuals act without thinking about social interaction

with others, and vice versa.

5.2.1 Identity as socially constructed

Social theories of learning are one starting-point for research on teacher iden-

tity and its formation. One approach is to consider identity in relation to posi-

tioning in a particular context as well as regarding power issues in develop-

mental process, as Gee (2000) states. Gee (2000, p. 99) defines identity, the

general sense of ‘being recognised as a certain kind of person’ in a given con-

text. In his analysis of identity, the central question is how and by whom a

particular identity is to be recognised. According to Gee (2000), identity can

be perceived from four points of view: (1) a state of existence that is given by

nature and is not under the control of an individual or an institution, (2) an

institutional position by which identity is recognised (e.g., a teacher in

school), (3) individuality, as an individual trait that is constructed through

discourse and interaction with others but determined by an individual, not by

external forces (see also Danielewicz, 2001), and lastly, (4) identity based on

being a member of an affinity group that shares common interests and prac-

tices (e.g., those who are interested in ice-swimming are members of a ice-

swimming club). In the case of becoming a teacher, all three latter aspects

could provide insight into the process. However, individuality describes the

phenomenon in a good way, especially within pre-service teacher education,

better than those involved with belonging to some affinity group or having a

position in the community.

In research on mathematics education, Wenger’s model of community of

practice (1998) is widely used as a basis for a social perspective on identity

(e.g., Bohl & van Zoest, 2002; Garcia, Sánchez, & Llinares, 2006; Hodgen &

Askew, 2007; Walshaw, 2004). Here, the outline and theoretical notion of

community of practice are discussed in order to have an idea of the social

approach to learning and identity formation. However, as the focus of the


research is on individual internal processes and the boundaries of internal and

external processes, the introduction is kept to a general level.

Wenger (1998) states that identity is developed through learning as a

member of a community of practice. The meaning of social communities is

essential to the process from the viewpoint of the social theory of learning. In

Wenger’s model, identity, meaning, practice, and community are all defined

and related to each other through learning. Wenger (1998, p. 4) underlines the

meaning of participation for constructing identities, as he claims that ‘such

participation shapes not only what we do, but also who we are and how we

interpret what we do’. The social theory of learning points up identity as a

way of talking about how learning changes who we are and creates personal

histories of becoming in the context of our communities. Wenger (1998, p.

145) claims that ‘building an identity consists of negotiating the meanings of

our experience of membership in social communities’. Thus when the defini-

tion of individuality is something that is part of the practices of specific

communities, identity is seen as the interplay between individual and collec-

tive rather than a distinction between these two dimensions (see also

Eteläpelto & Vähäsantanen, 2006; Swennen et al., 2008).

Wenger (1998, 148) extends the picture of identity through five notions:

(1) identity in practice, (2) identities of participation and non-participation,

(3) modes of belonging, (4) identification and negotiability, and (5) learning

communities. The parallel between practice and identity yields a perspective

on identity that is rich and complex because of its relations with practice. As

is essential for this process, he examines different modes of belonging to and

participation in a community of practice (see also Danielewicz, 2001).

Wenger (1998, p. 164) claims that ‘we not only produce our identities

through the practices we engage in, but we also define ourselves through

practices we do not engage in’ (see also Reid, Dahlgren, Petocz, & Dahlgren,

2008). Non-participation is also meaningful for identity formation as a

source. He separates three different modes of belonging in a community.

Firstly, he starts with engagement in practice that involves actions and inter-

action as well as shared reality and the negotiated meanings of experiences.

Wenger talks about the physical limits of time and space in order to distin-

guish engagement from other modes of belonging. Secondly, imagination is

an important component for the creative process of producing new ‘images’

and generating new relations. He underlines that imagination is not only an

individual process but is also related to social interactions and shared experi-

ences. In addition, although imagination can involve stereotypes and some-

thing that is not true, it is necessary for creating something new and project-

ing our experiences (cf. Atkinson, 2004). Thirdly, alignment, like imagina-

64 Heidi Krzywacki

tion, is not based on mutual engagement. Alignment requires that perspec-

tives and actions be directed toward common purposes, and individuals be-

come a part of something larger through discourse and acting according to

particular styles.

Similarly, Danielewicz (2001, pp. 114–123) elaborates the affiliation and

collaboration associated with social interaction in identity formation. She

situates her notions about affiliation in the teacher education programme and

teaching practice in the school, claiming that affiliation is a species of

socialisation which takes place through several functions, such as identifica-

tion, differentiation, and institutional actions upon identity. Danielewicz

states that identity is manifested individually, but exists in social categories.

In this sense, becoming as well as being a teacher involves developing both

an individual and collective identity, and these should be fostered simulta-

neously.

Similar to Wenger’s ideas, the relation between identity and learning new

knowledge and skills is seen as essential for identity development (see, e.g.,

Boaler & Greeno, 2000; Burn, 2007; Smith, 2007; Volman & ten Dam, 2007;

Beijaard et al., 2004). In a socio-cultural framework, as Wenger (1998) men-

tions, learning as a form of participation in communities of practice is not

only about learning new skills and knowledge but also involves identity de-

velopment (see also Lave & Wenger, 1991). In the study by Volman and ten

Dam (2007), since learning is seen as being able to participate increasingly

more adequately in social and cultural practices, it is linked to identity devel-

opment (see also Swennen et al., 2008). Knowledge and skills to be learned

should have a social connotation that students can identify with, because oth-

erwise they will not be integrated into identity. Volman and ten Dam (2007)

argue that learning and identity are related in two ways. First, identities are

developed through the learning process when students acquire new knowl-

edge and skills, and thus enhance their participation in social practices.

Second, identification with particular positions in social practices either en-

hances or inhibits students’ learning. Similarly, Garcia et al. (2006) associate

learning with participation in the community. In their study about teacher

educators’ development and practice in the mathematics community, learning

is seen as the growing use of conceptual tools, which are concerned with par-

ticipating in the community, including negotiation of meanings.

The social perspective of identity needs consideration. Firstly, identity is

elaborated as a general concept in social theories, e.g., by Wenger (1998) and

Volman and ten Dam (2007). Being a social being is seen as fundamental to

learning and, furthermore, as Wenger (1998, 145) states, building identity is

associated with negotiating the meanings of experiences as a member of


social communities. However, there is a difference between identity in gen-

eral and identity associated with a particular profession, like being a teacher.

The concept of ‘identity’ needs to be elaborated in more detail in applying it

to ‘becoming a teacher’. Experiences and communities of practice like

teacher education and school communities are of special interest (e.g.,

Coldron & Smith, 1999). Besides, the learning process as well as belonging

to a community is directed towards a particular outcome, ‘becoming a

teacher’, and the special knowledge and skills needed as a mathematics

teacher.

Secondly, the basic perspective in social theories is collective. An indi-

vidual develops through learning in the community and what the individual

engages with in interaction with others. Experiences and the meaning of con-

textual issues depend on each individual; for example, through choices and

the strength of engagement (Côté & Levine, 2002; Danielewicz, 2001). In

this research, the special interest is student teachers who go through their

developmental process in teacher education with special features.

Thirdly, modes of belonging are crucial for development as a teacher, the

notion being that a community of practice can become a learning envi-

ronment only if those three modes of belonging are combined effectively

(Wenger, 1998). The context of teacher education can be seen as one of the

communities that student teachers are engaged in and within which the pro-

cess of becoming a mathematics teacher operates. A student participates in

various communities of practice, teacher education being one. The ideal case

is that teacher education as a community of practice would be a learning en-

vironment in which the ideal image of a mathematics teacher offered in the

study programme as well as actions and interaction fits into the personal tra-

jectory for identity formation. Becoming a member of a school community is

also fundamental to the process of ‘becoming and being a teacher’ (Daniele-

wicz, 2001, pp. 111–130). However, in teacher education, students are more

members of a community of teacher education than of a ‘real’ school com-

munity. School as a community of practice has a minor part in this phase of

the process because of the limited amount of teaching practice.

5.2.2 Contextual influences

A contextual perspective is one way to approach professional identity, focus-

ing on constructions of professional identity in academic communities

(Archer, 2008), the teaching profession within social traditions (Coldron &

Smith, 1999), development of teacher identity in a changing educational en-

66 Heidi Krzywacki

vironment especially related to cultural issues (Samuel & Stephens, 2000),

and the significance of contextual forces (Assaf, 2008; see also Goos, 2005).

Research on identities situated in contextual framework has concentrated on

both sociological and political issues as well as special features of the envi-

ronment in which individuals participate (Collinson et al., 2009; see also

Settlage et al., 2009). The present focus is on the significance of contextual

issues such as traditions and environmental influences for professional iden-

tity development.

Identity formation can be regarded as socialisation into the teaching pro-

fession. From the collective viewpoint, the focus is on the influence that tra-

dition and shared conceptions have on individual development. An individual

has to be able to handle various educational traditions and to adapt within

contextual influences. In Côté and Levine’s model (2002), the relationship

between social and personal identity level deals with socialisation processes

(see Figure 2). Coldron and Smith (1999) list four larger social traditions that

form the social space in which the individual makes craft, moral, artistic, and

scientific choices, traditions which illuminate different aspects of being a

professional teacher. Coldron and Smith claim that a narrow view of ‘good

teaching’ should be avoided, and that teachers should be aware of a plurality

of approaches to teaching, beside being able to think critically. Assaf (2008),

who examines professional identity from the socio-cultural perspective,

thinks that contextual forces are essential for shaping teacher identity through

interpreted experiences. Shifting professional identity is seen as a response to

contextual forces in the school environment described under three main cate-

gories: professional beliefs, instructional practices, and the school context

including the teacher’s roles.

One should not see traditions simply as restrictive social structures, but as

the way to socialise in becoming and being a teacher (J. Cohen, 2008). Tradi-

tions are important for understanding and modelling issues arising from prac-

tice. Coldron and Smith (1999) use the term ‘active location’ in their analysis

of the construction of teacher identities in social space, which they define as

the range of possible choices an individual must make. They approach the

socialisation process by defining the relationship between agency and social

forms (see also Freitas, 2008). Professional identity is located as a dynamic

and not fixed phenomenon in the social environment, and ‛being teacher is a

matter of being seen as a teacher by himself or herself and by others; it is a

matter of acquiring and then redefining an identity that is socially legiti-

mated’ (Coldron & Smith, 1999, p. 712; see also Gee, 2000). They engage

MacLure’s idea (1993) that identity is something that an individual uses in

relations with other people. An individual’s location, professional identity, is


a socially given meaning for socialisation, and it is determined biographically

through personal choices. Samuel and Stephens (2000) examine the socialisa-

tion process in changing educational environments, conceptualising changes

through cultural, political, historical, and social significances. Identity is seen

as a tool for coping with contextual factors and the possibly controversial

demands that individuals face in the educational community. Samuel and

Stephens emphasise the importance of cultural influences for the professional

environment and the cultural context influencing teacher role identity.

In all, external demands and personal aspirations are both driving forces

in the development of teacher identity (Brown, 2003; Walkington, 2005; As-

saf, 2008). Both Brown (2003) and Freitas (2008) have examined changes

that take place in student teachers’ views of conceptualising mathematics and

its teaching. Student teachers seem to be reluctant to change their views of

teaching and learning mathematics despite activities provided to disrupt their

preconceptions. Besides, Brown (2003) claims that social practices cannot be

separated from personal engagement which involves emotional reactions re-

lated to mathematics. The meaning of the teachers’ own voices in participat-

ing in their own professional rationalities is essential. According to Brown, it

is problematic when social practices force the individual to move strongly in

a particular direction, and at the same time, individuals are obliged to pro-

duce their own teacher identity. Freitas (2008) highlights the importance of

critical awareness of existing collective understanding of teaching and learn-

ing.

Some notions regarding contextual factors of school practice and teacher

education emerge in the literature (e.g., Danielewicz, 2001). According to

Davies and Ferguson (1997), teacher education fails to address the needs that

emerge from the school reality, like dealing with behavioural problems and

cooperation with parents. Both issues relate strongly to school reality and

cultural changes in education. Goos (2005) has examined how personal and

contextual factors in the classroom shape the pedagogical identity of a novice

teacher in the sociocultural framework. In her work, pedagogical practices

and beliefs that novice teachers have about integrating technologies into

secondary mathematics education are of interest. Teacher actions in the class-

room have been examined in the light of three zones based on Valsiner’s

model (1997): (1) the zone of proximal development associated with individ-

ual undeveloped but emerging skills (ZPD), (2) the zone of free movement

that is related to environmental constraints and facilities (ZFM), and (3) the

zone of promoted action which is about an expert’s guidance and the oppor-

tunity to promote actions (ZPA). The idea is that the three zones have to be

balanced in order to make development possible.

68 Heidi Krzywacki

However, as Atkinson (2004) claims, offering the proper learning envi-

ronment with stimulating activities for student teachers is not simple. Teacher

identity cannot be influenced directly nor can student teachers adopt all the

knowledge and skills offered during the teacher education programme.

Korthagen (2004) suggests appropriate interventions to influence the various

levels of presented in Bateson’s model. Only the learning environment and

behaviour of a teacher can be observed directly. In teacher education, the

formation of identity may be influenced through outer levels in four ways: (1)

by creating a suitable learning environment (environment), (2) by modelling

and contingency management (behaviour), (3) through instruction, training

and coaching (competencies), and (4) by conceptual-change approaches (be-

liefs). Attaining conceptual change is the most difficult. In order to do this, it

is important to be aware of what students bring with them and to stimulate

them to reflect on their personal beliefs and experiences (see also Walking-

ton, 2005).

5.3 Boundaries between internal and external

In the review of the on-going process of identity formation, the process of

‛becoming a teacher’ has been approached separately from the internal and

external perspectives. Both are needed for the elaboration of teacher identity

formation (Beijaard et al., 2004). The boundaries between external and inter-

nal processes need to be examined here. In Côté and Levine’s model (2002),

it is the interactional level and engagement in activities of everyday life that

intermediates external and internal processes.

The notion of ‘going public’ (after Danielewicz, 2001, p. 60), i.e., that an

individual engages with interaction through self-presentation as a teacher, is

essential. Danielewicz (2001) emphasises the meaning of public involvement

and the role of an individual in making the process of ‛becoming a teacher’

visible to others. Once a person declares a desire to become and be a teacher,

other people start to take this into account as well. Since an individual is con-

sidered to have an active role in identity formation, commitment to the de-

velopmental process and taking a role as a teacher in public is important, as

Knowles (1992) states. The concept of ‘going public’ refers to conscious ac-

tions towards interaction, but as Gee (2000) points out, the process of en-

gagement in interaction with others and positioning oneself also has deliber-

ate, conscious, active, or tacit dimensions. Interaction with others is condi-

tional on uncovering the inner process to a certain extent by an individual.


Confronting the boundaries between individual and social levels of iden-

tity necessitates the idea of manifesting the state of identity to others through

self-presentation (after Côté & Levine, 2002). In the case of student teachers,

one way to manifest one’s own state of teacher identity is to take a role as a

mathematics teacher in the classroom. As well as being situated in the spe-

cific classroom context, it is a shared and lived experience in interaction with

others above all (after Wenger, 1998). Practical experiences and the oppor-

tunity to see oneself as a teacher are regarded as essential for formation of

emerging mathematics teacher identity during pre-service teacher education

(e.g., Danielewicz, 2001; see also Kagan, 1992; Knowles, 1992). The auth-

ority associated with a role as a teacher is something that a teacher should

have over students. According to Danielewicz (2001), it means the power

required to educate effectively as a teacher manifested in classroom control.

Danielewicz (2001) uses the concepts of public self and private self to

distinguish between internal and external processes (cf. ego and personal

identity in the model by Côté and Levine, 2002). Student teachers need to be

recognised as teachers by others and, in addition to this public image, should

be able to combine both social and individual perspectives of identity without

severe conflict. How well internal and external perspectives interconnect with

each other is especially meaningful for the person who is engaged in the de-

velopment process. As Samuel and Stephens (2000, p. 478) conclude, a

teacher should develop a professional identity which ‘sits comfortably with

their sense of self and maintain a balance between satisfying the requirements

of state and society and providing the source and impetus for change’. How-

ever, manifesting a state of teacher identity is problematic for students if they

are unaware of their being and needs as prospective teachers (Danielewicz,

2001; see also Arnon & Reichel, 2007).

Identity formation, or identity-making after Danielewicz (2001), is an it-

erative and recursive process. An individual reflects on his or her own being

and the state of identity on the basis of feedback and the responses of others

(e.g., Beijaard et al., 2004; Jenkins, 2004). Danielewicz (2001) describes the

process as a series of try-outs including representations, seeing others’ reac-

tions, and receiving feedback, revising, and then re-representing. Danielewicz

points out that interaction takes place through communication as well as

other activities during teacher education (see also Gee, 2000). The notions of

similarity and difference with others are at the heart of identity (Jenkins,

2004; see also Gee, 2000). Individuals shape and reshape their identities

through identification as well as through distinction. Similarity and difference

from others can be considered as an external force for reshaping identity as

well as something that makes the state of identity recognisable. As Daniele-

70 Heidi Krzywacki

wicz (2001, p.10) discuss, we all form notions of others based on categoris-

ing, simply comparing similarities and differences.


6 Research questions

This chapter sets out the research questions, starting from the original re-

search task formulated at the very beginning of the procedure. This qualita-

tive educational research was originally designed to answer the question

‘What is the process of teacher identity formation like in mathematics teacher

education?’ However, since only in the later phase of the research was the

understanding of the researcher clear enough to formulate more specific re-

search questions, the chapter defining the research questions is located here

after reviewing the research literature.

Teacher identity manifests itself through the three levels presented in

Côté and Levine’s model (2002), in which the interplay between an individ-

ual and others in a particular context was seen as essential for identity forma-

tion. However, even if identity is both individual and social, an individual is

the one to identify with and be identified with becoming and being a teacher.

An individual has a leading role through constructing a professional identity

and being the one who becomes a teacher through the processes that take

place in a social environment (e.g., Beijaard et al., 2004; cf. Wenger, 1998).

Consequently, the interplay between the context and the individual is related

to how one attains teacher identity and constructs an understanding of it. The

present approach is conceptual (after Beijaard et al., 2004), meaning that it is

possible to examine teacher identity through conceptualisation of one’s own

understanding. The original approach to teacher identity was based on Gee’s

idea (2000) that identity is something recognised by an individual self as well

as by others at a particular time and place. An individual is seen as one who

has primary access to the inner processes of identity formation. S/he is able to

conceptualise an understanding of the state of teacher identity as well as what

the understanding of others is. Furthermore, others indirectly influence the

developmental process through social interaction and, similarly, the mediated

social understanding of being a teacher may be attained through conceptuali-

sation. Teacher identity can be approached only through conceptualised un-

derstandings of one’s state as a teacher.

The research questions have been formulated based on comprehension of

the nature of teacher identity formation which has emerged from theoretical

conceptualisation in the literature. In the theoretical part, teacher identity has

been approached through three main perspectives: characterisation of teacher

identity, the significance of the image of the ideal teacher directing the devel-

opmental process, and the notion of an on-going process of teacher identity

formation. In fact, the overview of research literature has already addressed

72 Heidi Krzywacki

some of the need to understand the process of identity formation by con-

structing a theoretical conceptualisation for examination. Three main notions

proved to be crucial to teacher identity formation on which the research ques-

tions are based. Both individual and social perspectives are revealed through

these notions.

Characterisation of teacher identity The first subset was characterisation of teacher identity that forms a basis for

discussing what is associated with being a professional teacher in general and

what is actually recognised by the individual and others. Characterisation

makes it possible to discuss teacher identity, from both an individual and

social perspective (see Beijaard et al., 2004; see also Fajet et al., 2005). Two

subsets of characteristics associated with teacher identity, cognitive and af-

fective, were defined based on research literature and the contextual features

of the teacher education programme, within which identity formation is ex-

amined in this research. The state of teacher identity may be profiled through

different aspects, i.e., considering the meaning of each characteristic as a part

of the whole image. What is seen as desirable and valuable feature of a

teacher is value-bounded in relation to the context. In this research, the con-

text of Finnish teacher education and shared conceptions of being a good

teacher have been influential. The first research question is

How is teacher identity profiled through its cognitive and affective aspects?

Approaching teacher identity through the present and ideal images

The significance of the image of the ideal teacher was the second theme used

to approach teacher identity. The main idea in identity formation is the

change towards something, here the intention to become a (good) teacher. On

the one hand, an individual constructs an understanding of being a teacher by

reflecting on the present state (‛How am I at the moment?’) and the desired

state of teacher identity (‛How would I like to be in future?’) (Sfard &

Prusak, 2005; see also Beijaard et al., 2004). The process of change is under-

stood as closing the gap between these two states. From the individual per-

spective, the image of the ideal teacher, i.e., what is seen as desirable to as-

pire to, paves the way for individual development. However, the way the

ideal image directs individual development is dependent on how strongly it is

linked with personal goals that the individual sets. An individual has an ac-

tive role in setting personal aims for further development. On the other hand,

the ideal image is seen as a level at which individual and social aspects have

Research questions 73

an interface. Through social interaction, an individual becomes acquainted

with socially shared conceptions of the ideal teacher and, furthermore, re-

shapes his or her own understanding by filtering social influences (Côté &

Levine, 2002). From the social perspective, the focus of the research is on the

image of the ideal teacher that is provided in teacher education. The second

research question is thus

How do the present image of teacher identity and the image of the ideal

teacher shape the process of teacher identity formation?

The on-going process of teacher identity formation The third subset concerns teacher identity as an on-going process of change.

Teacher identity is seen as a dynamic and continuously reshaped entity that is

elaborated in the socio-psychological framework (Côté & Levine, 2002; see

also Bohl & van Zoest, 2002), which can be examined through concep-

tualised understandings of the notions of becoming and being a teacher. The

on-going process involves both internal processes and external processes that

function in social interaction with others. On the one hand, an individual con-

structs a subjective understanding of reality in terms of internal processes,

filtering socially mediated influences and internalising them as a part of his

or her own view. Previous internalisations and personal background as well

as previous experiences are essential in this process (Nelson, 2008; Samuel &

Stephens, 2000). The individual gives meaning to experiences through which

the changes in understanding of teacher identity take place. On the other

hand, identity formation is a socially embedded process, taking place in the

teacher education programme in this research. Contextual influences such as

the meaning of traditions and socialisation processes have an important role.

Boundaries between external and individual levels are of interest (Daniele-

wicz, 2001). An individual engages with social interaction by manifesting his

or her own state of teacher identity through everyday life, and is conse-

quently able to reflect on this state as a teacher based on the feedback. In this

research, the formation of teacher identity is understood as a series of chan-

ges in understanding of the state of emerging teacher identity. The third re-

search question is

What is the formation of emerging teacher identity like from the viewpoint of

change?


7 The case study approach

I discuss now the paradigmatic background of this research in order to articu-

late the underlying assumptions of this kind of educational research, qualita-

tive case study. As Guba and Lincoln (2005) state, inquiry methodology is

not simply a set of universally applicable rules or abstractions. They bring up

the major issues confronting all paradigms clearly, which are the ontological,

epistemological, and methodological bases (see also Denzin & Lincoln,

2000; Lincoln & Guba, 1985). These are the issues which need to be ad-

dressed in any underpinning research paradigm, including case study research

that is not related to any particular research paradigm, as Luck, Jackson, and

Usher (2006) suggest (see also Stevenson, 2004; VanWynsberghe & Khan,

2007). Luck et al. (2006, p. 108) in the context of nursing sciences argue that

‘case study offers a flexible, pragmatic yet rigorous approach to research that

is practical and suitable for nursing research’. The starting-point here can be

considered to be educational practice.

Case study as an educational research approach is understood in various

ways. According to Stake (2005), case study is a particular choice of what is

to be studied. The case itself is the issue as well as what can be learned about

it. Bassey (1999) argues that the educational case study approach is espe-

cially useful for developing educational theory that illuminates political and

educational practices (cf. Patton, 1997). He identifies three subsets of case

study: (1) theory-seeking and theory-testing case study, called instrumental

by Stake (1995) (cf. Yin, 2003), (2) story-telling and picture drawing case

study, called intrinsic by Stake (1995) and descriptive by Yin (2003), and (3)

evaluative case study, which is regarded as a basis for the case study ap-

proach adopted by Patton (1997). My instrumental interest in the formation

of teacher identity was the starting-point for constructing the study design

and carrying out the research procedure. The focus of the case study is on the

phenomenon itself, especially the formation of emerging teacher identity that

takes place during the programme, and the use of empirical cases is for

understanding this contextualised process better. Patton (2002) calls this

basic educational research.

The origin of this research was a practical interest in understanding the

process of becoming a teacher within a particular teacher education pro-

gramme. As Biesta and Burbules (2003) state, alluding to John Dewey, the

point in doing educational research can be regarded as getting at knowing the

practical phenomenon better as well as improving educational practices (see

also Patton, 1997 and 2002). Even if this research neither aims at directly

76 Heidi Krzywacki

evaluating or improving educational practices, practice, as exemplified in the

particularities of the cases, has been the point of departure (see Stake, 2005).

Furthermore, since characterisation of teacher identity and being professional

is context bound, it is possible to draw conclusions for improving the pro-

gramme based on the findings. Pragmatism is seen as influential for the

study.

7.1 The paradigmatic background of the research

Even if this research is not engaged with a particular paradigmatic back-

ground, pragmatism directed the way the research was originally conducted.

Pragmatism can be seen as emerging primarily from writings of three Ameri-

can thinkers from the end of the 19th

century and the first decades of 20th

: C.

S. Peirce, W. James, and J. Dewey. According to Biesta and Burbules (2003),

Deweyan pragmatism proposes neither a specific procedure for conducting

educational research, nor any specific research method. The pragmatist per-

spective is that the transactional framework allows us to understand know-

ledge as a function of and for human action, and human interaction and

communication in thoroughly practical terms. Although pragmatism is not

discussed here as a philosophical tradition in itself, the most important con-

sequences of pragmatism for educational research and for designing case

study research need to be considered. Firstly, according to Biesta and Bur-

bules (2003), the relationship between action and knowledge appears in the

attempt to refine and support day-to-day practice. Moreover, objects of

knowledge are then instruments appropriate in dealing with the everyday

problems. This also leads to bypassing the questions related to reconciling

‘scientific truth’ with ‘everyday life truths’. Secondly, the relationship be-

tween educational research and educational practice is not traditional. In

other words, the question is not about applying theoretical information to

practice but of cooperation and coordination (see also Stake, 2005). Thirdly,

pragmatism provides a way of thinking about the objects of knowledge as

instruments for action and, furthermore, different objects and different per-

ceived worlds provide opportunities for action. Finally, intersubjectivity is

the issue instead of objectivity and relativism.

The case study approach seemed to be appropriate for the research, the

way to achieve understanding of teacher identity formation. According to

Stake (2000), the power of the case study approach is capturing the case as a

bounded system and exploring experiences in practice (cf. Yin, 2003). It pro-

vides an opportunity to extend our direct experiences. Reality is seen to con-

The case study approach 77

sist of experiences and perceptions of all those, both teacher educators and

students, involved in the study programme. This research is associated with

an interpretive and naturalistic approach, sometimes called the constructivist

approach, as the main idea is to understand unique individual experiences

that take place in social interaction and are given meaning in social reality

(Bassey, 1999; Stake, 1995). There is no single truth as all perspectives are

meaningful and valued in the process of examining the case. Furthermore,

there is no one ideal way to develop as a teacher. However, the case study

approach enables one to see issues through a researcher’s eyes and add theo-

retical construction to experiences (Donmoyer, 2000).

However, as Puolimatka (2002) suggests, pragmatism is problematic be-

cause of its basic idea of truth. Truth is based on utility and usefulness in

practice, somehow combining ‘scientific truth’ with practical truth. Stake

(1995) describes qualitative research of this kind as a non-determinist and

constructivist approach. Qualitative inquiry used as a research approach is

subjective and intersubjective as well as rather open (cf. Patton, 1997). How-

ever, it is a challenge to conduct research in such a way and to manage to find

truth in that sense. A criticism of case study research is the disadvantages of

the kind of knowledge that is obtained. From a traditional perspective, gener-

alisation has been a problematic issue to be confronted in research of this

type (e.g., Flyvbjerg, 2006; Hammersley & Gomm, 2000). Case study is

about capturing the particularities of the case, about understanding the

bounded system itself. Controversy between the emergence of generalisation

and the particular case is insuperable. By contrast, Lincoln and Guba (2000)

discuss transferability and fittingness, which are defined as congruence be-

tween the context of the research and the context to which the results could

be applied. Related to the possibility of achieving truth, Puolimatka (2002)

also mentions that, despite the problematic issues related to reliability and the

theory of truth, educational reality is accessible to some extent based on eve-

ryday experiences through qualitative research.

7.2 Methodological choices

A description of the issues related to study design and methodological deci-

sions appears in what follows. As Hammersley and Gomm (2000) point out,

there is no standard way to do case study. In this research, case study is seen

as a method and a research strategy rather than a paradigm (Stake, 1995). In

an instrumental case study like this (after Stake, 2005), the case is of secon-

dary interest, playing a supportive role and facilitating our understanding of

78 Heidi Krzywacki

something else. However, the case is explored thoroughly and the context is

elaborated to enhance our understanding. After defining the purpose of the

research, the case(s) need to be defined and boundaries set for data collection

(Stake, 1995). Students and teacher educators illuminate the process of

teacher identity formation in two ways. Individual development is elaborated

through the student perspective, those who become teachers. Each case as a

whole has been considered in order to be able to understand the meanings of

these contextualised experiences.

The case of teacher educators has been composed collectively to illustrate

the social environment in which individual development is situated. The em-

pirical part of the work is based on multiple cases.

First, depending on the purpose of the research, a case study might be

either qualitative or quantitative in nature (Yin, 2003). In this research, the

purpose has been influential for research design and qualitative strategy,

meaning that naturalistic inquiry based on qualitative data and content analy-

sis has been chosen in order to learn about identity development through in-

dividual experiences (Patton, 2002). Practical issues, not simply a need to

understand developmental process have influenced the decision-making. Fur-

thermore, as Hammersley, Gomm, and Foster (2000) remark, multiple case

studies allow us an insight into causal relations and knowledge that could be

generalised theoretically. In this research, multiple cases are examined to

better understand the patterns of student teacher development and the role of

the programme in supporting development.

Second, the inductive approach, where the researcher is interested in each

participant’s experiences without delimiting or pigeonholing, provides a

point of departure. The research does include, however, elements of the de-

ductive strategy, as examination of the phenomenon is outlined in terms of

the theoretical framework of teacher identity formation which is augmented

by practical notions. The aim is to merge the patterns related to teacher iden-

tity formation in the programme rather than impose some predetermined,

deductively derived construction. As Stevenson (2004) points out, description

of the case by using abstract concepts and a theoretical framework needs to

be transparent enough to transform knowledge for others and to be obedient

to the authencity of experience.

Third, the relation between partial and holistic approaches also appears in

the case study approach (Patton, 1997). As Stake (2000) states, particularities

of the case are of interest. Each student case here forms a bounded system

with its own particularities. Description of the social perspective, however, is

formed collectively and particularities make sense as part of the whole. A

researcher needs both holistic and partial approaches at the same time.


Fourth, as it concentrates on identity formation and ‘what is really hap-

pening’, the research might be described as naturalistic by nature (Patton,

2002; see also Stevenson, 2004). However, it is not purely naturalistic be-

cause of the data-gathering process and the presence of the researcher, which

might possibly have an effect on the student teachers. Intentional manipula-

tions were avoided in order to have an opportunity to have a look at typical

procedures within the programme, even if the study design can be seen as

creative and practical. Furthermore, the view of change in this research is

dynamic (Patton, 1997). The approach to identity formation was action orien-

tated and aiming at revealing developmental outcomes in the formation pro-

cess.

Last, Stake (1995) claims that interpretation is a major part of all re-

search, especially in a case study. The researcher draws conclusions on the

basis of the data gathered. Furthermore, he describes a good case study as

reflective, patient, and willing to see another side of the research issue. Fun-

damentally, the researcher tries to preserve the multiple realities, the intersub-

jective world according to Biesta and Burbules (2003), sometimes even con-

tradictory views. Thus, the researcher matters.

7.3 The role of the researcher in the research process

My own role as a researcher needs to be described in order to help readers to

see my potential influence on the research process and to be able to evaluate

the study (Stake, 1995; Tuomi & Sarajärvi, 2002). Some researchers regard

this as the basis of confirmability of the research that needs to be discussed as

a part of its trustworthiness (Miles & Huberman, 1994). The role of the re-

searcher intertwines with subjectivity and biases in research with an inter-

view process both in the interview situation and in the analysis phase (Seid-

man, 1998; see also Kvale, 1996) Stake (1995) emphasises the various roles

that a researcher might have in course of the process. The roles through

which I clarify my stance relate to relationships between the phenomena, the

participants, the researcher, and readers of the report.

Firstly, Stake (1995) identifies the case researcher as a teacher who tries

to teach readers about the case and find the right words in order to compre-

hend. The researcher’s role in informing others and in delivering knowledge

gained through the research is essential. Here, the relationship between the

researcher and members of both scientific community and teacher education

is essential. I worked as a junior researcher in the Department of Applied

Sciences of Education (the former Department of Teacher Education) starting

80 Heidi Krzywacki

in 2003. Beside research activities, I have also been responsible for teaching

pre-service primary school teachers in mathematics education and supervi-

sion in a teaching practice school. However, I have not been involved with

subject teacher education as a teacher educator but as a coordinator in co-

operation between partners responsible for the teacher education programme

(Lavonen et al., 2007). Therefore, testing draft ideas and preliminary findings

with potential readers has taken place in seminars for developing the teacher

education programme, for example.

Secondly, the case researcher might be seen as an advocate. In reporting

the study, a researcher tries to convince readers of conclusions that have been

drawn and the reasons for them. Some values underlying interpretation need

to be declared. My basic education, which must have influenced my stance as

a researcher, is in both educational sciences and university mathematics. I

originally graduated as a primary school teacher, but I also have experience

in studying university level mathematics as a major subject and philosophy of

life as a minor. Based on my own experience as a student, both teacher edu-

cation and mathematical education are familiar and easy to identify with.

However, I have not experienced the particular teacher education programme

of this research through personal participation, either as a teacher educator or

as a student. I regard my position as an outside member of the community of

subject teacher education as helpful in understanding and interpreting the

cases.

Thirdly, the case researcher can be seen as an evaluator (see Stake 1995).

The role of a researcher in qualitative research is central when the emphasis

is on the quality of activities and processes, portraying them in narrative de-

scription and conclusions based on interpreted evidence (e.g., Patton, 2002;

Seidman, 1998). Knowing various aspects of the programme has been of help

in the research as well as being acquainted with all the actors. In this matter, I

have presented my ideas and preliminary study not only to make them more

understandable but also to make sure that those responsible for implementa-

tion of the programme are aware of my project and have an opportunity to

comment. The role as evaluator is particularly relevant in research on teacher

identity formation and the phenomena that need to be recognised by the indi-

vidual and by others (Gee, 2000).

Stake (1995) promotes the idea of the case researcher as biographer and

interpreter, which concerns the interrelations between the participants and

the researcher. The researcher is seen as an agent of new interpretation and

new knowledge. My task has been to describe in detail the separate student

cases, like story-telling, thus giving readers an opportunity to evaluate my

research and interpretations. Each student case comprises a bounded system


approached holistically. The basic interpretation and reporting the cases is

grounded on gathered interview data but, in order to improve my interpreta-

tion, I have also taken a close look at additional data and tried to picture each

case based on informal knowledge and fleeting notions through interactional

contacts with them. A researcher should guard against writing to fit a stereo-

type (Stake 1995; see also 2005). In describing the processes of each student,

my intention was to take into consideration the meaning they gave and how

they saw the process. My own experience and understanding of the contex-

tual influences have helped in this process.

Altogether, firstly, experiences in mathematical education and educational

sciences in the pre-service teacher education have surely influenced my un-

derstanding of the individual processes. However, the process that students

get involved in during the teacher education programme is not so familiar as

to prevent examining it openly. Secondly, my experience as a teacher educa-

tor has been of help in understanding and constructing the reality from the

teacher educators’ viewpoint. Thirdly, my role as a coordinator has been es-

sential for the research project, especially my ability to interpret and make

contacts with the research participants. These three roles combined together

have been crucial to my ability to carry out the research in meaningful way.

7.4 Conclusions concerning the paradigmatic background

This chapter has dealt with the paradigmatic background of the research and

the foundation of methodological choices in qualitative case study, starting

with the idea that this instrumental case study is embedded in the framework

of pragmatism. The meaning of three aspects related to epistemological and

ontological views are essential according to Biesta and Burbules (2003).

Firstly, the relationship between theory and practice needs to be discussed.

Theoretical knowledge is intertwined with practice and one cannot discuss

them separately – objects of knowledge can be seen as doing rather than

knowing something. This interplay is reflected in the design of the present

case study and, as Biesta and Burbules (2003) claim, through the research

procedure. This occurs in transforming the particularities of the cases into

systematic and conceptual form. Secondly, the relationship between know-

ledge and reality, the idea of objects of knowledge as opportunities and possi-

bilities for action, is specially addressed in methodological choices. Study

design and defining the research question reflect the multiple perspectives of

various participants, not only through selecting a different kind of research

participant, like students and teacher educators, but also through resources

82 Heidi Krzywacki

resources and choices in the data analysis. My role as a researcher is to

intermediate this intersubjectivity. Thirdly, the question about the nature of

knowledge that is seen as intersubjective according to Biesta and Burbules

(2003), is contextual and practical and, most importantly, always related to

foundational aims and values (cf. Stake 1995; see also Patton 1997). In all,

educational research is fundamentally for education, and educational know-

ledge should lead to more intelligent practice.


8 Conduct of the research

This chapter describes the overall view of the research procedure, including

the cases, data-gathering process, and analysis. First, the research context that

influences the whole process, especially defining the cases in the study, is

portrayed. The selection of cases is then discussed and the data-gathering as

well as data handling and analysis processes are elaborated in detail. Lastly, a

summary of the research procedure concludes the chapter.

8.1 Defining the research cases

This qualitative case study consists of multiple cases, those of student teach-

ers as well as teacher educators. The research context has to be well known to

be able to design the data construction and before that, choose the cases to be

examined (Stake, 1995). The reasons for sampling and making practical deci-

sions have to be described clearly in order to explain the contribution that the

participants make to the research particularly (Patton, 2002). According to

Miles and Huberman (1994), defining the case(s) not only concerns people as

research participants but situations and context to be examined. The context,

here the teacher education programme at the University of Helsinki, and the

research task are both influential in the selection of the cases and for the

overall study design. The practice is an essential starting-point for a case

study of this kind.

The data is based on insights provided by two kinds of participant: stu-

dents who are actually becoming teachers and whose professional identity

develops, and teacher educators, who are seen as purposeful informants on

the contextual and social surroundings. Consequently, the selection of the

cases differs. As Schofield (2000) states, the possibility of generalisation

should be considered when selecting the cases, and in his opinion, something

typical, ordinary and common should be investigated, and careful case selec-

tion should reveal something new from such typical cases (cf. Flyvbjerg,

2006). Thorough description of the case and the context clarifies how and

why it is seen as typical (Patton, 2002). Only then is generalisation within the

context possible (see also Stake, 2005). However, systematic selection of

typical cases is associated with the idea of being able to describe the whole

body of possible cases and their typical features (Hammersley et al., 2000).

Beside selecting the cases for their typicality, information-oriented selection

is one possibility according to Flyvbjerg (2006). The cases are then selected

84 Heidi Krzywacki

on the basis of the potential to cover various perspectives of the research con-

text.

In this research, ‘mainstream’ students for whom the study programme is

mainly designed were selected for the student cases. This kind of strategy

suits well with the idea of testing and completing the theoretical framework

(Flyvbjerg 2006; Yin, 2003). Multiple cases are needed to enhance researcher

understanding of processes and phenomenon more generally (Miles & Hu-

berman, 1994). The teacher educators, however, who gave an insight into the

study programme, were deliberately selected with an information orientation

(Patton, 2002). The teacher educators represent the various viewpoints on the

context in which individual formation takes place. Since the point was to get

a coherent view of the study programme, research participants were selected

according to their positions in the programme. Each student case represents

an individual case, through which development is examined, as in instrumen-

tal case study defined by Stake (1995). However, the teacher educators form

a collective case study in which the shared understanding of teacher identity

is the key issue.

8.1.1 Mathematics teacher education as a research context

The mathematics teacher education programme is outlined to provide an

overall view of the research context. First, since the formation of teacher

identity is examined focusing especially on the early steps in becoming a

mathematics teacher, several courses and modules of the teacher education

programme are described to establish the context within which student teach-

ers act. Even though formation of professional identity is not merely influ-

enced by teacher education or restricted to the official educational frame-

work, elements and activities of the study programme are considered to be

essential for identity formation. Second, in addition to its influence on indi-

vidual development, the research context has had an impact on the design of

the research and on the usefulness of the findings.

The research is on mathematics student teachers who will be qualified to

teach mathematics and another school subject, like chemistry or physics, in

grades 7–9 in the lower secondary school (students of 12–16 years old) and

grades 10–12 in upper secondary school (students of 16–19 years old). At the

University of Helsinki as well as other Finnish universities, master’s studies

in university mathematics are the main component of the mathematics

teacher education. The programme consists of a master’s degree pre-service

Conduct of the research 85

teacher education programme (300 cp1), which takes approximately five or

six years to complete (see Figure 3). The programme consists of mathemati-

cal education, i.e., university mathematics as a major (150 cp), another school

subject such as chemistry or physics (60 cp), and a year of education (60 cp)

including supervised teaching practice modules (20 cp). In addition, the pro-

gramme includes language and communication courses.

Figure 3. The structure of the teacher education programme at the University of Hel-

sinki

Some essential features of the programme are discussed in more detail be-

cause of its importance for the research. The Department of Mathematics and

Statistics is responsible for mathematical education, which is the same for all

bachelor’s level mathematics students despite their intended specialisation. In

master’s courses, the aim is to deepen students’ knowledge of real numbers

and analysis in general. However, two special mathematical courses are pro-

vided for prospective teachers at master’s level; one course on geometry (10

cp) and another for student teachers focusing on integrating university math-

ematics with school content (12 cp). Mathematical content knowledge

courses are based on the same structure as other university programmes in

1 1 credit point (cp) means approximately 27 hours work.

160

Minor subject

Bachelor’s level (180 cp.) Master’s level (120 cp.)

Masters’ thesis

Educational studies

Major subject

Credit points

Communication and language

studies

180

140

100

120

80

60

40

20

0

Ed. thesis

86 Heidi Krzywacki

mathematics as a discipline. The notions about the students’ need for help in

learning university level mathematics and in combining separate pieces of

mathematical knowledge together has led to improvement in tutoring of all

students (Oikkonen, 2009; see also Lavonen et al., 2007).

As illustrated in Table 1, the educational studies are divided into four sec-

tions: general educational courses (13 cp), mathematics education (17 cp),

educational research (10 cp), and supervised teaching practice periods (20

cp). The main idea is to help students to combine educational theories with

practice and their previous knowledge of mathematics. The need to combine

theory with practice is to be addressed by combining different courses to-

gether through timing and contents. In addition, portfolio assessment work is

also used to help students form a coherent view of what is provided during

the courses. (Lavonen et. al, 2007)

Table 1. The structure of the educational courses in mathematics teacher education

programme

General courses in education, teaching and learning (13 cp)

Mathematics education (17 cp)

Educational research (10 cp)

Teaching practice (20 cp)

Psychology of de-

velopment and learn-

ing

Special needs educa-

tion

Social, historical,

and philosophical

basis of education

Psychological basis

of teaching and

learning mathemat-

ics

Curriculum devel-

opment and planning

of teaching

Evaluation of teach-

ing and learning of

mathematics

Research methodol-

ogy in education

The teacher as a

researcher seminar

Minor thesis in edu-

cation

Supervised teaching

practice (basic, ap-

plied and advanced)

Reflection supported

by portfolio assess-

ment work

Although students may apply for the teacher education programme at each

phase of their studies in mathematics, the courses (60 cp) provided by De-

partment of Applied Sciences of Education are usually completed after the 4th

or 5th

year because of the structure of the programme. The constraint is that

students have to complete enough courses in mathematics and another school

subject, like physics or chemistry, to ensure that they have sufficient exper-


tise in content knowledge before entering the first teaching practice period at

the end of the first half of the educational studies.

The main organising theme of the research-based teacher education is to

promote the teacher’s pedagogical thinking. In other words, being a profes-

sional is not only based on expertise in separate knowledge domains, like

mathematical content knowledge and pedagogical knowledge, but also on

being able to apply such knowledge and skills in practice (Kansanen et al.,

2000; Lavonen et al., 2007). The teacher education programme can be de-

scribed as a highly academic way to educate prospective teachers when cog-

nitive knowledge and skills are critical to the research-based programme.

Firstly, in practice, all mathematics student teachers complete both a master’s

thesis in their major subject (30 cp) and a minor educational thesis as a part

of their courses in mathematics education within the educational studies (10

cp). The aim is to achieve thinking skills both regarding subject matter and

pedagogical issues as well as skills for continuous professional development

in the future. Students not only deepen their understanding of central con-

cepts and familiarize themselves with research literature and methods, but are

given an opportunity to experience being a reflective practitioner, as a profes-

sional who may act as a researcher in future work (see also Westbury et al.,

2005). Secondly, the teaching practice is included only in the educational

study year, and students have responsibility for no more than approximately

50 hours of lessons.

8.1.2 Student teachers

The student participants were selected among those taking a major in math-

ematics and who had decided to become a teacher, i.e., those who wanted to

specialise in teaching and learning mathematics through educational studies

as their minor subject. In practice, student teachers participate in university

mathematics courses at the Department of Mathematics and Statistics (sub-

ject department) among all other mathematics students, especially for the first

three or four years. Moreover, only some mathematics students make a deci-

sion on future specialisation at the beginning of their university studies. The

majority settle on teacher education after a couple of years at university. The

student teachers who participated in the research were selected among so-

called mainstream students in mathematics teacher education, whose needs

the programme is primarily designed to address. There are also special

groups of students who do educational studies after their master’s degree in

mathematics or engineering, for instance. However, because of differentiation

88 Heidi Krzywacki

in their educational backgrounds, which is not specifically considered in the

programme, concentrating on mainstream students was a conscious choice.

First, all mathematics students able to participate in the research, i.e. those

students taking a major in mathematics and who participated in most educa-

tional courses during the academic year 2005–2006 had to be found. The

students also had to be willing to participate in the research. In practice, be-

cause of the structure and timing of the programme, these students could be

reached in early autumn just at the beginning of the educational studies. In

order to contact all the possible participants, the researcher visited the first

small-group meeting for portfolio assessment work by mathematics student

teachers. The research project and the main idea were briefly introduced to

the students (Appendix 1). In this phase, the role of the researcher, the posi-

tion as a staff member with no direct involvement, particularly with the

secondary teacher education programme, was clarified. After the introduc-

tion, students were asked to write about themselves as a student (Appendix

3). Based on the information given, all possible voluntary students, 21 alto-

gether, were contacted. Three dropped out of the educational course during

the first semester, leaving 18 students as research participants altogether.

To ensure that there were enough participants by the end of the academic

year, the data was gathered from all eighteen. It was already obvious that

only a few cases could be included in the research report. The selection was

based on the research task and contextual features. First, students with special

status or an exceptional educational background, like a doctoral degree and

university degree in engineering, were excluded in order to focus on so-called

‘mainstream’ cases that the teacher education programme is primarily de-

signed for. Then, as further selection was needed, two were chosen on the

grounds of their background information and general familiarity with the

possible cases. The idea was to capture two student cases through which

teacher identity formation within the teacher education programme could be

examined. In practice, the first two cases with sufficient conceptualisation of

the developmental process were selected in order to assure the emergence of

the phenomenon.

There are two reasons for this solution. First, by selecting two ‘main-

stream’ student cases, the nature of teacher identity formation could be exam-

ined embedded in the context of teacher education (Schofield, 2000). The

case study approach is intended to uncover processes and patterns of individ-

ual cases, using the case description to make transforming the findings pos-

sible but not to generalise anything in a traditional way (Lincoln & Guba,

2000; Stake, 1995 and 2005). Furthermore, as Grossman (1990) has argued

for her study design, since teacher development always involves an individ-


ual, expanding the number of cases would not meet the requirements of gen-

eralisation. On the other hand, the selection had to be made before thorough

data analysis because of the practical constraints of time and other resources.

Without specific and in depth understanding of all cases based on data analy-

sis, the cases to be elaborated in detail were selected by chronological order.

Two cases, John and Mary, are presented in this research report. Even

though the results are not based on comparisons between individual images

of each student’s teacher identity, some general notions about their back-

grounds at the beginning of their educational studies can be of help in show-

ing who the student research participants were (Table 2). First, at the begin-

ning of the course, the research participants differed from each other because

of their various motivational backgrounds. John was somewhat uncertain

about his motives for applying for the teacher education programme. He had

originally wondered what subject his personal interest would be. Mathemat-

ics became his major subject during his university studies. He pointed out

that the meaningful learning experiences he had had in mathematics itself

were the reason for his choice. Furthermore, becoming a teacher provided

him with an opportunity to have a real occupation. The case of Mary is dif-

ferent, as she was motivated and stated that becoming a teacher was her first

choice. The only decision she made was whether to become an elementary

school teacher or a secondary school mathematics teacher. Second, neither of

the students had work experience as a substitute teacher. This is understand-

able because of their ages; at the time of the research, John was 29 years old

and Mary 25. Third, both were taking a mathematics major and, by chance,

physics as a minor subject to be taught in school. However, their back-

grounds differed regarding previous studies in education. John had done

some educational studies beforehand but Mary had not.

90 Heidi Krzywacki

Table 2. Background of the student participants John and Mary

John Mary

Motivation for applying for the teacher education programme

John is a strongly self-

regulated student who wants

to study issues of his own

interest. He regards himself

as suitable for the teaching

profession but it is only one

possibility among others for

him. One reason for becom-

ing a teacher is pragmatic, as

he discusses the opportunity

to have a job in the future.

Mary has always wanted to become a

teacher. She hesitated only between

whether to apply for elementary or

subject teacher education. According to

Mary, she drifted into studying univer-

sity mathematics after graduating from

high school with good marks. She be-

came inspired by mathematical educa-

tion and decided to combine her desire

to become a teacher with this particular

subject.

Work experi-ence as a teacher

John does not have teaching

experience in school, only

some experience in giving

private mathematics lessons

Mary does not have teaching experience

in school, only some experience in lei-

sure activities with youngsters

Age 29, started university in 1997 25, started university in 2001

School subjects (major and minor sub-jects)

mathematics and physics mathematics and physics

Previous stud-ies in education

previous studies in general

educational sciences (no

specific teacher education

courses)

no previous studies in education at all

8.1.3 The collective case of teacher educators

The other perspective for the process of teacher identity formation was based

on conceptions of teacher educators, who were involved in the mathematics

teacher education programme. The idea was to examine the overall view of

becoming and being a mathematics teacher provided during the study pro-

gramme through aim setting and study implementation. Each teacher educa-

tor has conceptions of becoming and being a good (mathematics) teacher,

relating both to the ideal image in general and study activities that should

procedure individual development. However, since the individual teacher


educator has a limited opportunity to influence and interact with students

within the teacher education programme, the conceptions of teacher educa-

tors as a whole are of interest.

Information-oriented selection based on particular criteria, purposeful

sampling according to Patton (2002), was used (see also Flyvbjerg, 2006).

The mathematics teacher education programme is somewhat fragmented be-

cause of multiple subjects and rather small courses in different topics. As the

idea of sampling was to select teacher educators so as to represent all sections

of the programme, the structure of the programme and the different courses

were the starting-point. Therefore, all educators responsible for teaching,

mentoring or planning the programme were regarded as possible participants

for the research, approximately 60 teacher educators altogether.

In practice, a teacher educator who would be a good informant in the re-

search was the one with an opportunity to influence the programme imple-

mentation through teaching and planning. Each teacher educator in question

was listed according to the various sections included in the programme. First,

all sections of the programme, mathematical education in the Department of

Mathematics and Statistics, teaching practice in university practice schools,

and both mathematics education and general educational studies in the De-

partment of Applied Sciences of Education were to be represented. Second,

those teacher educators who had a central role in the programme implementa-

tion and had participated in co-operation in programme development were

highlighted. Furthermore, the selection was not only based on the number of

lesson hours or their official position in the programme but was also influ-

enced by the role that individuals have in developmental co-operation be-

tween university partners. An information letter was sent by e-mail to the key

persons who were selected to be the participants (Appendix 2). The only

challenge in selection was to find the key informants for mathematical educa-

tion, because only a couple of courses are provided specially for mathematics

student teachers and people in charge of the courses change almost every

year. All educators included in the original selection agreed to participate in

the research.

The collective case of teacher educators has been gleaned from interviews

with 11 participants altogether. All sections of the programme, and by the

same token, all partners involved in the programme, were represented: math-

ematical education relating to studies in university mathematics (2), general

educational studies (4), mathematics education (2), and teaching practice (3)

included in the section of educational studies. As one can see, the selection of

the research participants is not based on the amount of study according to

credit points but on the idea to gather data that would reveal influences on

92 Heidi Krzywacki

teacher identity during teacher education as richly as possible (Patton, 2002).

Next, a brief overview of each participant is given to show what kind of key

informant the collective case is based on (Table 3).

Table 3. The background of the teacher educators

TE Role in the teacher education programme Department represented

TE1 responsible for the course in special needs

education

Department of Applied Sciences of

Education

TE2 responsible for the course in general education Department of Applied Sciences of

Education

TE3 responsible for the course in analysis Department of Mathematics and

Statistics

TE4 responsible for the advanced course for student

teachers

Department of Mathematics and

Statistics

TE5 teaching practice supervisor University teaching practice school

TE6 teaching practice supervisor University teaching practice school

TE7 teaching practice supervisor Teaching practice school

TE8 responsible for the course in developmental

and learning psychology


Education

TE9 responsible for the courses in mathematics

education


Education

TE10 responsible for the course in the philosophical,

sociological, and historical basis of education


Education

TE11 responsible for the courses in mathematics

education


Education

Teacher educator 1 (TE1) was responsible for the course in special needs

education as a part of subject teacher education for the first time. According

to him, the topic of the course was his speciality through previous teaching

experience as a university lecturer and research activities, but the context of

subject teachers was something new. Despite the experience as a teacher edu-

cator and research-based knowledge about the topic, TE1 felt that the frame-

work of the course was too broad and a challenge for a single person. Conse-

quently, TE1 had a real need for co-operation with other educators in plan-

ning the course content and for discovering the coherence conception of the

study programme. Framing the course especially for prospective subject

teachers seemed to be a challenge for him. Besides, he claimed that it was


essential to take into consideration the background of subject student teach-

ers, e.g., work experience and study history.

Teacher educator 2 (TE2) was responsible for a course in general educa-

tion. He had wide experience as a teacher educator in all pre-service teacher

education courses as a professor of general education. TE2 emphasised his

essential role in implementation and further development of general educa-

tion as a part of teacher education. TE2 was worried about the marginal role

of general educational issues in the teacher education programme for secon-

dary school teachers. TE2 did not find co-operation with other teacher educa-

tors essential, the reason being the busy schedule and, more importantly, that

there is no special need for co-operation because of the clear framework for

different courses and division of responsibilities in programme implementa-

tion.

Teacher educator 3 (TE3), who represented the Department of Mathemat-

ics and Statistics, had long experience as a mathematician and researcher as

well as university teaching experience in mathematics. Mathematics is his

main motive for involvement in teacher education, but he has become inter-

ested lately in development of teacher education and teaching mathematics.

In fact, it is not obvious whether TE3 should call himself a teacher educator

or not. Courses on bachelor level mathematics are for all mathematics stu-

dents despite their intended specialisation. To be a teacher educator is more

likely to involve administration like marking and supervising master’s theses.

However, TE3 finds cooperation with other teacher educators relevant, even

if he thinks the individual teacher educator has a minor role and limited op-

portunity to exert influence.

Teacher educator 4 (TE4) also represented the Department of Mathemat-

ics and Statistics. For TE4, teaching and being a teacher educator was as im-

portant as research on mathematics. Furthermore, TE4 had taken a degree in

pedagogy for higher education as a part of his university work. However, as

was the case with TE3, T4 did not categorise himself necessarily as a teacher

educator in being responsible for courses in university mathematics for all

students. He has been one of the active participants in cooperation to develop

teacher education representing the mathematics department, but he still stated

that cooperation with other teacher educators had no central role in his work,

which is more about educating all mathematics students in general and

teacher education is only marginal.

Teacher educator 5 (TE5) was a supervisor at a university teaching prac-

tice school, both in lower and upper secondary school mathematics. He em-

phasised a strong commitment to his work and willingness for further devel-

opment as a mentor, beside being a mathematics teacher. TE5 had a couple of

94 Heidi Krzywacki

years’ experience as a mentor. He described his role as an educator as di-

vided: while he felt like a mentor during teaching practice periods, he felt

more like an ordinary teacher at other times. Personal needs, which should be

addressed if possible, should be the basis in mentoring the students. TE5

found cooperation within the teacher education programme valuable, espe-

cially with other mentors in university practice schools.

Teacher educator 6 (TE6) was an experienced teacher educator with a

long career at a university practice school. He was also responsible for teach-

ing upper and lower secondary school mathematics, beside being a mentor

for student teachers. He prioritised his role as a mathematics teacher over

being a teacher educator. In practice, pupils in the classroom always come

before the needs of teaching practice as part of teacher education. In general,

TE6 described his role as a teacher who also does his share in the teacher

education programme. He valued cooperation with other teacher educators.

He claimed that more detailed and clear standards for mentoring and evaluat-

ing students would be of particular help. TE6 seemed to regard his role as a

teacher educator as personally meaningful.

Teacher educator 7 (TE7) represented the so-called ordinary field school,

in which teaching practice periods, especially the second practicum called

applied teaching practice, takes place. He worked as a mathematics teacher in

secondary school for a couple years after graduation before taking a role as a

mentor. TE7 stated that it is easy for him to identify with the role of the

mathematics student teacher. Taking a role as a teacher educator was also an

opportunity for him to reflect on his own activities in the classroom but, first

and foremost, he highlighted the importance of teaching practice periods for

individual development of students. He also saw cooperation with other

teachers as a resource.

Teacher educator 8 (TE8) was responsible for the course in develop-

mental and learning psychology in the subject teacher education programme.

Beside the general course for all student teachers, he had also a role as an

educator for psychology student teachers. He had been involved in teacher

education for approximately for the last ten years in all. In his opinion, his

expertise is especially about issues related to interaction and about how to

educate students’ skills for social interaction. TE8 discussed the lack of time

for doing research because of teaching obligations. Cooperation with other

teacher educators has occurred, especially with others responsible for the

developmental and learning psychology course.

Teacher educator 9 (TE9) represented the Department of Applied Sci-

ences of Education, especially the courses in mathematics education. She was

one of the educators responsible for the studies in mathematics education


including portfolio assessment work, the educational minor thesis, and

courses in mathematics education and methods. She had long and extensive

experience in teaching mathematics both at school and university. Beside

practical experience, she was also active in the educational research com-

munity, which was one of her reasons for becoming a teacher educator. It was

also an opportunity for self-development. Cooperation with other teacher

educators was one part of her role as an educator. Interaction with teaching

practice mentors was of particular significance.

Teacher educator 10 (TE10) was responsible for the course in the philo-

sophical, sociological and historical basis of education in all teacher educa-

tion programmes at the Department of Applied Sciences of Education. This

experienced teacher educator originally transferred to work at the university

because of his desire to complete his doctoral dissertation in history educa-

tion. The development of the course in question has been his responsibility

for several years. According to the interview, TE10 has taken the implemen-

tation of the course as a challenge because of the large number of students

and the extensive framework of the course content. However, his role as a

teacher educator has been meaningful as TE10 is able to teach in his research

field. Collaboration with other educators was restricted to those who are re-

sponsible for the group activities of the course.

Teacher educator 11 (TE11) represented the modules of mathematics

education. TE11 was an experienced teacher educator in mathematics educa-

tion with a mathematical background and long experience in pre-service

teacher education. In practice, TE11 was responsible for the course in the

educational minor thesis and lectures in mathematics education in the pro-

gramme. TE11 is intimately engaged with research activities, and regards it

as possible to really know something only through research. Educational re-

search, especially on mathematics education, was seen as strength for him as

a teacher educator. Co-operation with other teacher educators takes place

mainly within his own research group. However, TE11 reflected on the need

for more general discussion on values and the principles underpinning the

teacher education programme.

8.2 The data-gathering process

As Stevenson (2004) states, pre-structured cases including pre-designed data

collection procedures are needed to ensure that investigation is focused expe-

diently (see also Bassey, 1999; Huberman & Miles, 1994). The data that the

cases are based on was compiled during the 2005–2006 academic year. Some

96 Heidi Krzywacki

decisions had to be made about research procedure, especially the nature of

data required and the timetable for the data-gathering process. Firstly, the

empirical part of the research comprises two kinds of cases, student cases and

the collective case of teacher educators. Semi-structured interviews were

considered to be the appropriate approach (see Kvale, 1996). According to

Seidman (1998, p. 7), the interview is ‘a powerful way to gain insight into

educational issues through understanding the experience of the individuals

whose lives constitute education’ (see also Kvale, 1996; Tierney & Dilley,

2002). Furthermore, the interview data was augmented with written docu-

ments to improve interpretation. This data revealed the conceptualisation and

reasoning of participants and facilitated seeking data triangulation (e.g.,

Bassey, 1999; Seidman, 1998; Stake, 2005).

Secondly, data-gathering was completed during one academic year,

2005–2006, during the educational studies that student teachers participated

in. Two reasons justify this decision. First, the courses lasting two semesters

are practically the only ones targeted specifically at the teaching occupation.

Only a few courses in university mathematics are specialized for student

teachers, and in practice the process of ‘becoming a teacher’ is considered

mainly in the educational studies. Second, the one-year timetable for data-

gathering was a practical choice. Because of the structure of the university

courses, particularly when specialisation in teaching usually takes place dur-

ing the last two years, contacting student teachers would have been practi-

cally impossible before they took their educational studies. For many student

teachers, the process of becoming a teacher starts only then.

8.2.1 Interviews

The procedure for interviews with student teachers and teacher educators is

described separately. The way interviews were designed and what was dis-

cussed is particularly significant for understanding the cases, and thus, for

understanding teacher identity formation (e.g., Seidman, 1998). Kvale (1996)

points out that there are no special rules, procedures or techniques to be fol-

lowed (see also Keats, 2000). It is about making decisions on the reflective

level, based on knowledge of the field, particularly in accordance with the

research purpose (Stake, 1995).

Interviews with the student teachers Student teachers participated in three semi-structured interviews during the

2005–2006 academic year, similar to the setting of the study by Settlage et al.


(2009). The idea of making student teachers reflect on their conceptions and

experiences of becoming and being a teacher remained the same in all three

interviews. The structure of the interviews, especially the first, was designed

on the basis of experiences that the researcher had had in a preliminary study

in autumn 2004 as well as research literature about teacher development, as

Seidman (1998) suggests. The preliminary research was on student teachers’

views on the teacher education programme, especially educational studies as

part of the programme (Krzywacki & Juuti, 2005). The data was gathered

through semi-structured interviews with ten student teachers. In designing the

structure and situational arrangements of the interviews, it was useful to have

experience in interview situations and in forming questions beforehand. Car-

rying out the semi-structured interviews without leading the interviewees was

particularly considered.

Before the first interview, all participants were given a brief information

letter about the research (Appendix 1). In addition, the first interview was

settled on the phone and some discussion took place depending on what the

participants wanted to know more about. The role of the researcher and the

confidentiality of interviews were explained to the participants. The second

and the third interviews were rather similar, the first one dealing with the

main issues and arrangements for the interview situations. The student teach-

ers were thus able to build up a schema of the interview situations and the

procedure beforehand based on the first interview. In practice, all interview

meetings were carried out at the Department of Applied Sciences of Educa-

tion, the idea being to make participation in the research as easy as possible.

Students were able to integrate the interview meetings with their study activi-

ties and no extra effort was needed in this sense. Even more importantly, the

aim was to establish an atmosphere in which the participants could feel free

to talk about their experiences (Kvale, 1996).

The first interview with the student teachers was based on four themes re-

lated to being a good mathematics teacher and becoming a teacher during the

programme (Appendix 4). The reason for carrying out the first interview right

at the beginning of the educational studies was to elicit conceptions of be-

coming and being a teacher before the influence of the courses, particularly

the teaching practice periods, in which all students teach under supervision.

First, the motivational background for applying to the teacher education pro-

gramme was of interest. Students were made to reflect on their reasons for

becoming a teacher as well as to talk about their educational history. Second,

expectations and personal aims for the courses were discussed in the two

phases of the interview. Third, discussion on the conceptions on teaching and

learning mathematics started with a question related to school memories, and

98 Heidi Krzywacki

experiences in school mathematics. Even if that was not the particular topic

of the research, it was a good phase to start further discussion of being a good

mathematics teacher and, more importantly, for questions related to the kind

of mathematics teacher the interviewee wanted to become. Specific skills and

knowledge were discussed as being related to conceptions of a good math-

ematics teacher. Last, students were asked to reflect on their view of the best

way to evolve into a good mathematics teacher.

At the second interview, which was carried out just before the Christmas

break in December 2005, expectations and the main issues of the previous

interview connected to the programme were summed up with the student in

order to enable discussion of the courses so far in terms of preliminary expec-

tations (Appendix 5). The idea of a good mathematics teacher as well as the

features of a good teacher generally was discussed again. In addition to gen-

eral reflections, students were asked to reflect on themselves as a teacher

through their strengths and issues of further development. Students also

talked about personal goals in their upcoming studies and in school work.

Since the second interview was conducted after five months of their course, it

was natural to evaluate the work done so far in respect of their own experi-

ences as a student teacher.

The third interview took place at the end of the educational studies in the

spring of 2006. The exact time of the last meeting depended on the final

teaching practice period. The last teaching practice lesson(s) of each student

teacher were observed before carrying out the last interview. The lessons

were recorded, not for use as research data but to share the experience with

the participants before the last interview. The students got the video record-

ing of their lessons for their own use at the last meeting. The themes of the

semi-structured interview were basically the same as in the two previous

ones. Three main themes were under discussion: the notion of a good math-

ematics teacher, evaluation of the programme, and reflections on the stu-

dent’s own development as a prospective teacher (Appendix 6). Plans for a

career were also of interest.

The student interviews, which took place three times during the academic

year, constituted the core of the data for the student cases. First, it is import-

ant that interaction between interviewer and interviewee be based on trust and

confidentiality (Kvale, 1996; Seidman, 1998). Spontaneous interaction was

promoted as the research participants and the researcher came to know each

other through several meetings during the study year and visiting one of the

teaching lessons during the advanced teaching practice period. Second, the

main themes were discussed in all three interviews. While the students had an

opportunity to return to these themes and change as well as stability of views


can be seen in the data, the previous interviews and discussions about the

same topics had provoked the students’ thinking. Being conscious of one’s

own thinking was needed when the data was based on the student teacher’s

ability to conceptualise personal development and general conceptions of

teaching and learning mathematics, especially being a good teacher (Beijaard

et al., 2004). In this sense, one cannot regard the continuous procedure of the

research as harmful for the validity of the data. Moreover, the times between

each interview, approximately three and five months, were long enough for

students to forget the details of the previous interview. Only the main themes

recurred to them. Last, the interviews were carried out with the idea that stu-

dents were mostly to make the running, the input as well as the comments by

the researcher being minimised (see Seidman, 1998). This worked out well,

especially with multiple interviews.

Interviews with the teacher educators The main theme of the interviews with teacher educators was about concep-

tions of becoming and being a good teacher. The special interest was their

role as a teacher educator, how the aims and implementation of the pro-

gramme supports individual development of mathematics student teachers

during teacher education. The semi-structured interviews took place in April

and May 2006 before the end of the semester. All participants were informed

about the topic of the research project in general (Appendix 2). However, no

further information or specific questions were brought up beforehand. The

idea was to elicit the personal theory and basic conceptions of all teacher

educators. Interviews based on questions and tasks given beforehand would

have produced different data. Replication of the written official curriculum

and documentation of statements that teacher educators would have regarded

as ‘the right answers’ was to be avoided.

The interview was initially structured around the themes discussed with

the student participants. The main discussions concerned theory derived from

educational literature, just as in the student interviews. Furthermore, although

the teacher educators’ stance on the process of identity formation differs from

the student perspective, no specific theoretical concepts related to the forma-

tion of teacher identity were used in the interviews. Consequently, the way

teacher educators talked about their role in the programme as well as about

becoming a good teacher was not provoked by the conceptualisation of the

researcher and, at least to some extent, the idea of juxtaposing reflections of

teacher educators with those of student teachers was already considered while

gathering the data.

100 Heidi Krzywacki

A few principles were adopted to address the different roles and back-

ground of teacher educators in the interviews. First, the structure had to allow

slight modification according to the interview situation and the issues that

might emerge individually (Warren, 2002). Only the main themes were the

subject of specific questions and further information was brought up when

needed. The roles of teacher educators and the significance of single courses

varied. For example, the role of a professor of educational science was sig-

nificantly different from an ordinary mathematics teacher involved in mentor-

ing during teaching practice periods. Second, the design of the interview was

slightly modified based on the preliminary interview with an experienced

science teacher educator. The four original themes remained the same, but

some questions were modified and themes on the role and the background as

a teacher educator were marked out for separate discussion.

The semi-structured interview was originally based on four main themes

(Appendix 7). First, the interviewee’s background as an educator was one of

the interview themes, and then the role in the teacher education programme.

Some warming up was needed at the beginning of the interview, and the

background and the role of each informant was needed for understanding

each teacher educator’s perspective. Second, conceptions of teaching and

learning in general were discussed. The perspective of the individual teacher

was preferred to describing teaching and learning situations. Discussion

about being a good teacher differed according to the teacher educators’ posi-

tion in the programme and whether mathematics as a discipline had an im-

portant role or not. However, the special interest in mathematics teachers was

brought up at least at a general level. Third, the relevance and the main idea

of subject teacher education were discussed through reflections on goals,

implementation and evaluation of the courses. The idea of the third section

was especially to elicit intentions which an individual teacher educator had

for guidance during teacher education. The courses and views of the whole

programme were discussed separately. The fourth theme was evaluation of

the programme and ideas for further development.

In practice, the semi-structured interviews were mainly the same with all

educators but the order of the themes and the number of follow-up questions

differed according to interaction and the interview situation. The follow-up

questions were needed only if an interviewee did not offer further reasoning

on that theme (Warren, 2002). The role of the researcher in relation to the

status of the interviewee was either collegial or hierarchical. In practice, the

social situation of each interview was formed from pre-existing dealings with

participants, and the situations turned out to be relaxed enough for such in-

terviews.


8.2.2 Supplementary material

Supplementary material was also used in order to obtain various viewpoints

and to confirm interpretations of the interview data (Stake, 1995; cf. Yin,

2003). In the student cases, written products like portfolio assessment work

were used to augment the overall picture. The interviews with teacher educa-

tors were juxtaposed with the written curriculum for the teacher education.

The cases of student teachers The supplementary data about the processes of the students during their edu-

cational studies included portfolio self-assessment work, an essay about

school experiences in mathematics, and feedback questionnaires completed

twice during the academic year. The self-assessment portfolios and some

other written products were initially supposed to have the more essential role

in giving an insight into individual development as a teacher. However, it

became clear during the research that written material could only be used as

additional source because of the nature of the products as part of the course.

First, in practice, the most essential source of supplementary material was

portfolio assessment work. Reflections related to teaching practice periods

were useful, especially about personal teaching practice aims when taking a

role as a teacher in the classroom and self-evaluation as a teacher afterwards.

Second, one way to gain an overall picture of evaluation of the programme

by the students and to interpret their attitudes toward their personal develop-

ment was to look at the feedback questionnaires about their courses. The

questionnaire was the same for all students who took the educational studies

during the 2005–2006 academic year. The main idea of the structured ques-

tionnaire was to assess study arrangements and the overall implementation of

the programme. Third, the essay about school experiences as a mathematics

student was written at the beginning of the course in mathematics education.

The task was to consider school memories in order to become aware of the

significance of previous experiences and to understand how one’s school

background might influence thinking. The most important thing was to ex-

tend the picture of an individual student and to have an opportunity to read

more about school experiences, especially when this was explicitly brought

up by the students.

The teacher educators’ perspective In addition to the data from interviews, the written curriculum for the secon-

dary teacher education programme at the University of Helsinki was used as

a complementary source on the conceptions of teacher educators. The main

102 Heidi Krzywacki

principles of the teacher education programme are documented in the curricu-

lum. Even if the research was not primarily about the context of the teacher

education programme itself but about formation of teacher identity within it,

the official curriculum provided another perspective on the central aims and

the image of the ideal teacher provided by the teacher educators. All teacher

educators involved with the programme implementation have done their

share in planning and writing the official curriculum which, including the

official aims and the description of the intended outcome, can also be re-

garded as a link between teacher educators and student teachers.

8.3 Data handling and analysis

The aim of data handling and analysis in case study research is to achieve

data reduction in order make it comprehensible (Huberman & Miles, 1994;

see also Tuomi & Sarajärvi, 2002). A researcher has to make decisions about

the data presentation, i.e. how the cases and results appear, and what kind of

role the theoretical framework has in the analysis and presentation of the re-

sults. In practice, the presentation of the data is related to the whole process

of empirical study, from the data-gathering phase to the final conclusions and

verification of the findings.

The role of theory and some practical circumstances have particularly af-

fected the way data analysis has been carried out and presented. Firstly, data

analysis was conducted only partly simultaneously with data-gathering, and

some practical challenges did not arise during the analysis. In describing in-

trinsic case study, Stake (1995) brings up problematic issues of carrying out

the data analysis alongside the research process and challenges in making

decisions about the procedure parallel with the field work. However, in an

instrumental case study (the concept used by Stake, 1995) like this, the de-

sign of the research procedure is not so much open-ended as pre-determined

regarding, for example, the cases of interest, timing of interviews, structure

of the interviews, and data presentations based on the theoretical background.

Besides, separating interviewing and analysis minimises imposing something

that emerged in previous interviews on the interview process, as Seidman

(1998) remarks. In the first place, the research task was not about responding

to immediate practical situations but understanding the ‘teacher identity’

phenomenon through several cases. In practice, the analysis took place

gradually from January of 2007 to April of 2008. The first interview data on

the student teachers was examined in November and December 2005 simply


in order to be able to discuss the initial expectations of the students in the

second interview.

Secondly, content analysis was chosen for the written and verbal data.

Content analysis can be used for quantitative or qualitative data, either in a

deductive or inductive way (Elo & Kyngäs, 2007; see also Hammersley &

Gomm, 2000). Here, the analysis has both deductive and inductive elements.

The way content analysis was carried out can be described as a modified ver-

sion of analytic induction, in which the original theory-derived categories are

modified through the analysis of separate cases (Hammersley et al., 2000;

Huberman & Miles, 1994; Tuomi & Sarajärvi, 2002; see also Patton, 2002;

cf. Elo & Kyngäs, 2007). The basis of data-handling and analysis was theo-

retical conceptualisation. In practice, understanding teacher identity and its

formation was originally extended through the review on research literature.

The themes of semi-structured interviews were formed on that basis and used

as initial categories in the analysis phase. The original categorisation of the

data was therefore established on the conceptualisation fixed beforehand. The

initial categorisation was reshaped gradually from case to case by systematic

procedure and researcher’s intuition alongwith the analysis. Theory and em-

pirical notions have thus been intertwined and influenced each other in both

directions.

Thirdly, the data is composed of two different kinds of cases, student

cases approached and presented individually and the case of teacher educa-

tors, approached collectively. The aim should be, as Miles and Huberman

(1994) discuss, to describe and explain the cases as well as to find some kind

of causality. The conceptualisation based on the theoretical framework was

used as the ground for presenting the case descriptions. Nevertheless, the aim

was not to find generalisability or particular patterns in the process of becom-

ing a teacher as would be the idea originally in analytic induction (Miles &

Huberman, 1994; see also Robinson, 2000). The cases themselves were of

interest, but the case descriptions rely on common conceptualisation. In other

words, all individuals have their unique developmental process but this can

be displayed through the common features of teacher identity.

The data analysis, qualitative content analysis procedure is presented here

step by step. As there were two kinds of data, interviews and supplementary

written documents, the description of data handling and analysis is presented

in two parts.

104 Heidi Krzywacki

8.3.1 Interview data

The data handling and analysis of the interview data of both teacher educa-

tors and students are discussed here side by side. There were only a few dif-

ferences in the analysis processes arising from the dissimilar roles of the par-

ticipants. In the student data analysis, the notion of change and the basic as-

sumption of an on-going developmental process were relevant, whereas

teacher educators gave an insight into contextual influences and the currently

desirable image of a mathematics teacher from a social perspective. How-

ever, the basic idea in content analysis was the same for both sources.

The data based on recorded semi-structured interviews was initially tran-

scribed as a whole. An outsider carried out this phase of the data handling.

Naturally, it was the researcher’s responsibility to make sure that the tran-

scriptions represented the original recordings. All transcriptions were

checked by listening to the tapes alongwith the transliteration, and the re-

searcher started to immerse herself in the data at the same time (Seidman,

1998; Kvale, 1996). Only a few mistakes and indistinct spots were corrected,

and the first impression of the whole dataset was gained through this revi-

sion. In practice, it was arranged that all indistinct expressions were specifi-

cally marked in the transliteration in order to assist correction.

The second phase of the analysis was to divide the transliterations into

units of analysis (Elo & Kyngäs, 2007; Miles & Huberman, 1994; Tuomi &

Sarajärvi, 2002). In order to be able to address the original research task, the

appropriate units of analysis needed to be defined, in this case units of flex-

ible length and larger than just separate sentences (see Patton, 2002). Frag-

mentation was to be avoided, and the connection with the context was im-

portant for understanding the reflections of the participants. The overall view

of the context was retained by using a unit of meaning which consisted of one

or more clauses as the analysis unit. In practice, the original transliteration

was read through the second time and was divided into units of meaning. The

following is an example on the original interview data of student Mary (S2).

127 H (H = interviewer) well how has it… was the teaching practice?

128 S2 that I have enjoyed practice very much, well I have been to *** high

school, which is pretty easy to do your practical training in cos there’s no prob-

lem with discipline, they [the pupils] are real motivated, motivated to study… so,

in that sense it’s been pretty easy to teach. But I think that it has been definitely

the best thing, teaching practice in the educational [studies]…

129 H ok, why do you think that? S2 well… I just like teaching so much and

it’s been real good to take lessons there, and without a doubt it plays a huge part

that the school is nice as well as the pupils, so, it has made me enjoy it … I think


that the chance to experience practice and to act as a teacher, do what you are

supposed to do, makes it more real and feels that this is really my thing, that it is

not just about reading stuff from books…

Some decisions regarding the units were made. All questions and comments

by the researcher which led to a new subject or brought something signifi-

cantly new to the interview situation were placed in separate units. This made

it technically possible to examine the structure of the interviews, and later the

validity of the data; e.g., how the researcher prompted the interview situa-

tions (Kvale, 1996; Warren, 2002). Follow-up questions, which were asked in

order to reveal reasons or to get more detailed information about something

under discussion, were situated in the same unit as the interviewee’s ideas.

The distinction was whether the researcher’s address was the initiative for the

interview process or not. Each unit was then numbered before transferring the

data from a word document onto an excel-sheet, in which the analysis was

carried out. The numbering made it easy to find the original data when

needed.

The third phase of the analysis was to formulate reduced expressions for

each unit. All student cases were reduced before continuing with the analysis

process. The idea of reduced expressions was to transform spoken expres-

sions into more readable form; e.g., to leave out expressions and mannerisms

with no special significance for the content. Along with producing reduced

expressions and reading the data for the third time, some notions and working

themes were written down. The original categorisation derived from the

interview themes was then in mind, but was used more systematically only at

the next phase of the analysis. As one can see in the sample of the data units

(Table 4), the original expression was situated alongside the reduced expres-

sion as well as with further categorising in order to make it easy to backtrack

to original phrases when needed.

Table 4. An example of organising the data and reduced expressions

N:o Original expression Reduced expression Preliminary notions and themes

127 H (H = interviewer) well how has

it… was the teaching practice?

How has the teaching

practice been?

128 S2 that I have enjoyed practice

very much, well I have been to

*** high school, which is pretty

I have enjoyed it very

much, I was *** and it

was an easy school be-

teaching practice

positive experi-

106 Heidi Krzywacki

easy to do your practical training

in cos there’s no problem with

discipline, they [the pupils] are

real motivated, motivated to

study… so, in that sense it’s been

pretty easy to teach. But I think

that it has been definitely the best

thing, teaching practice in the

educational [studies]…

cause there are no disci-

plinary problems and the

pupils are motivated to

study.

It has been easy to teach.

Teaching practice has

definitely been the best

thing in the educational

studies.

ence in practice

The teaching

practice experi-

ence the best thing

in the course

129 H ok, why do you think like that?

S2 well… I just like teaching so

much and it’s been real good to

take lessons there, and without a

doubt it plays a huge part that the

school is nice as well as the pu-

pils, so, it has made me enjoy it

… I think that the chance to ex-

perience practice and to act as a

teacher, do what you are sup-

posed to do, it makes it more real

and feels that this is really my

thing, that it is not just about

reading stuff from books…

I like teaching a lot and

it has been nice to take

lessons. Undoubtedly,

the pleasant school envi-

ronment and nice pupils

have helped me to enjoy

it. An opportunity to act

in practice. It is more

real and you feel you are

doing your own thing for

real, that it is not just

reading something in

books.

teaching practice

pleasant school

environment

enjoyment

acting as a teacher

and real school

experiences are

meaningful

The fourth phase of the analysis of student data was about categorising the

data according to the original categories and notions formulated in the previ-

ous round. There were originally five main categories in the student inter-

views: (1) a starting-point and the background of a student teacher; (2) con-

ceptions of good teaching and being a mathematics teacher (the ideal image

of mathematics teacher); (3) identification as a teacher; (4) expectations and

aims for the course, and (5) evaluation of the course in relation to personal

development as a teacher. At this phase, since it was clear that one analysis

unit might be categorised in more than one subset, the categorisation was not

exclusive either in the student cases or that of the teacher educators. The ori-

ginal categorisation was reshaped by sub-categories (see Appendix 8). In the

first version of the categorisation, the main structure remained after the first

round of analysis. However, the image of the ideal teacher and the individual

developmental process were still separate categories. The conceptions of

good mathematics teaching and learning were clarified by different subsets,

i.e., knowledge, skills and affective aspects associated with teaching and


learning (Features of a teacher), but identification with being a teacher was

approached at a more general level (View of self as a teacher).

Next, after examination of the next two student cases, some modification

took place in the categorisation system (Appendix 9). Firstly, separate know-

ledge and skills as well as affective aspects were grouped into two subsets,

the cognitive and affective aspects of becoming and being a mathematics

teacher. The cognitive aspects were divided into four sub-categories, three

related to teacher knowledge domains and one to thinking skills needed as a

teacher. The affective aspect was about personal features and attitude towards

teaching and professional development. Secondly, sub-categories related to

the teacher education programme were clarified and re-grouped. The issues

related to the learning process were brought up alongside various study mod-

ules. Thirdly, the structure based on the ideal and present images of being a

teacher was brought into the categorisation. Besides, cognitive and affective

aspects were further divided into two sub-categories, general views of being a

teacher and views of oneself as a teacher.

In the next phase, the sub-categories regarding the context of teacher edu-

cation and evaluation of the course were modified (categories starting from

400, see Appendix 10). However, given the research focus, the evaluation of

the teacher education was not of interest and is not reported here in more de-

tail. On completing categorisation of the cases, three main subsets were

formed: conceptions of teaching and learning mathematics, the personal pro-

cess of becoming a teacher, and the teacher education programme supporting

the individual process (Table 5, see also Appendix 11).

Table 5. The final version of the categorization (student cases)

Sub-categories The main category General conceptions of teaching and learning

Individual teacher and teacher competences

(a teacher as a person)

Conceptions of teaching and learning

mathematics

Background of a prospective teacher

Individual developmental process

Personal process of becoming a

teacher

Meaningfulness of and attitude towards the

course

Content and implementation of the course

The overall view of the course

Teacher education programme sup-

porting individual development

108 Heidi Krzywacki

In the final version of categorisation, the overall developmental process re-

lated to personal identification with the teaching occupation and the approach

to being a teacher through separate aspects were distinguished. In the former

category, the basis of grouping was in the overall process that a person goes

through when becoming a teacher and in those aspects that were associated

with the personal process generally. In the latter, the teaching occupation is

seen as separate competences, which define being a professional teacher.

Two examples are given to clarify the difference (Table 6). It is worth noting

that when categorisation of the units is not exclusive, the same unit may be-

long to one or more subsets.

Table 6. Examples of categorisation of analysis units

John (spring, 314)

Original expression Reduced expression Sub-category(s) H well… how would you evaluate your-

self as a prospective mathematics teacher

and also, already being one… what are

your strengths? S1 well… probably that…

that well… that I have pretty well estab-

lished a grasp of mathematical content

knowledge that I… that I understand what

it is about. I regard it as rather important,

well, maybe the most important virtue.

H Evaluate yourself as a

prospective mathematics

teacher, what are your

strengths?

S1 I have pretty well

established content

knowledge; I understand

the issues. That is prob-

ably the most important.

Mathematical

content know-

ledge: one’s own

starting-point as a

teacher

(111)

Mary (spring, 284)

Original expression Reduced expression Sub-category(s) H did this emerge in practice somehow?

S2 well… as a matter of fact I heard that

there are some people, already graduated,

who like keeping a diary after every les-

son, write down some notes in the margin,

that ‘this was a particularly difficult topic’

and then, the next time when taking a

lesson on the same topic, it is possible to

backtrack to the previous session and see

the issues that were difficult and think

over how to do it this time… I think that

I heard that one already

qualified teacher makes

notes, like keeping a

diary, in the margin of

lesson plans, about

whether something was

difficult. When you

teach the same topic next

time, you will remember

how to do it. I regarded

that as wise thing to do

pedagogical con-

tent knowledge

(120)

commitment to

development of

oneself as a

teacher

(230)


it’s something I’d like to do as well, it is a

clever thing to do and it is worth doing …

that I could have the feeling... I could

remember next year when teaching the

same topic what was particularly difficult

about it,

in order to have a feel-

ing… and I would re-

member next year when

the same topic comes up

again.

All cases were eventually categorised using the same system. However, this

was only the basis for further examination of individual cases. Since the

underlying assumption was that teacher identity and its formation is an

individual phenomenon, the analysis was continued by focusing on each

student case separately. From an individual perspective, the on-going process

that is essential for teacher identity was examined using the three separate

interviews side-by-side through various categories, the idea of change being

paramount (Beijaard et al, 2004; see also Richardson & Placier, 2001). The

notion of change needed to be defined for the data analysis. The students

themselves identified the change through self-reflection and their own con-

scious statements about it. However, since it is not always so conscious or

structured that individuals can reflect on it, individual change was also de-

fined by the researcher by examining the possible changes within categories.

Similarly, the relationship between the present image and the ideal image of

being a mathematics teacher which informs different aspects of the teaching

profession was of special interest. In the end, the two student cases are de-

scribed through the categorisation. Furthermore, as the developmental pro-

cess was of interest, the main category ‘the teacher education programme

supporting the individual process’ is not reported here in more detail.

The data-handling and analysis procedure of the teacher educator inter-

views were basically the same as with the student interview data. Because of

their different role in the research, the original interview themes were ar-

ranged differently. The basis of the data analysis was the four main interview

themes: (1) role as a teacher educator; (2) conceptions of teaching and learn-

ing mathematics; (3) one’s own course(s) as part of the study programme;

and (4) the overall view of the study programme. In the first phase, after pre-

liminary analysis of two first cases, only some minor modification of the

categorisation was done (Appendix 12). Two main categories emerged at this

phase of the analysis, the starting-point as a teacher educator and implemen-

tation of the study programme (Table 7). In the first main category, subsets

related to the teacher educator’s background comprised the first higher-order

setting. In the second, implementation of the course(s) that the teacher educa-

tor was responsible for was discussed separately from the overall view of the

110 Heidi Krzywacki

teacher education programme, the main idea being to identify issues to which

teacher educators could contribute or could not. Furthermore, the general

conceptions of a good (mathematics) teacher and the particular aims for stu-

dent teachers attending the courses were distinguished at this stage. These

two subsets naturally overlapped, but the idea was to distinguish between

personal views that teacher educators had and those that teacher educators

wanted to mediate through their courses.

Table 7. The final version of the categorization (the case of teacher educators)

Subsets The main category Role as a teacher educator

Conceptions of good teaching and learning

(in mathematics)

Starting-point as a teacher educator

Ones’ own course(s) as part of the pro-

gramme

The overall view of the study programme

Implementation of the teacher education pro-

gramme

The division of sub-categories comprising the higher-order settings was clari-

fied in the second phase, after analysis of four cases (Appendix 13). Firstly,

the relationship with students was removed to the subset of one’s own teach-

ing, and the sub-category related to student selection was created. Further-

more, a need to highlight the role of student teachers among all other students

emerged. The role as a teacher educator and visibility of student teachers

varied depending on the position that the teacher educator had in the educa-

tional system.

In the end, the original categorisation was revised only slightly, and the

final version was not significantly different from the original one (Appendix

14). The way the cases were finally to be presented influenced the process to

some extent. Firstly, the idea was to create a categorisation system through

which all cases of teacher educators, despite their positions in the educational

system and their role in relation to the students, could be described and ana-

lysed. Teacher educators were treated as separate cases to begin with. The

shared categorisation was needed to facilitate conclusions about the various

cases as one entity. Secondly, the categorisation of the data on teacher educa-

tors has features in common with categorisation of the students. In the origi-

nal interviews with both participants, conceptions of good teaching and learn-

ing as well as contextual features of the study programme had been dis-


cussed. These commonalities made it possible to juxtapose the cases and then

discuss them side-by-side.

In the next phase, each teacher educator was studied separately using the

categorisation, and case descriptions were created separately from each other

as a bounded system. The collective view of the teacher educators was then

constructed on the basis of these cases. In the collective case, the main issue

was related to implementation of the teacher education programme itself,

whereas the individual characteristics of the teacher educators, for example,

their overall conceptions of good teaching and learning, were used to help in

interpretation. After all, the research was not about the overall conceptions of

teacher educators and their personalities as educators but contextual and so-

cial influences in the teacher education mediated by them.

Member checking was used as all participants were asked to review the

case descriptions for accuracy and palatability (Stake, 1995; 2000; see also

Patton, 2002). Since no changes were made to the case descriptions, member

checking was more likely to assure mutual understanding and to inform the

participants about the outcome. Besides, the participants could only comment

on their overall impressions of whether the transcript reflected their personal

views or not.

8.3.2 Supplementary material

Material supplementing the interview data was examined in terms of the

categorisation systems created for the interview data. The supplementary data

was originally structural and expressions were polished more carefully than

in interview data, which meant that the analysis through categorical aggrega-

tion was suitable and there was no need to produce reduced expressions as

with the interviews (see Stake, 1995). The analysis of this material focused

on extending the understanding of the cases and on strengthening interpreta-

tion of the interview data. Supplementary material was thus used only in the

second phase of data analysis while producing the case presentations.

In practice, supplementary material such as portfolio assessment work

and feedback questionnaires of the student cases was read through several

times, and essential information highlighted by categorisation. Supplemen-

tary data provided insight into the developmental process that all students

were engaged with. However, a critical approach was essential because stu-

dents had produced the written documents as course requirements according

to special guidelines. The written documents were based on their self-

reflections but their production was to be evaluated by the teacher educators.

112 Heidi Krzywacki

According to the students, discussions in the portfolio assessment work were

mostly about their genuine reflections, but these were to some extent written

to meet the expectations of the educators. Critical viewpoints about the pro-

gramme and especially doubts about their development or motives for be-

coming a teacher were not elaborated openly. The issues of validity were

addressed through critical dissection. In practice, when the data on the inter-

views and the statements in portfolio assessment work were in conflict, dis-

cussions in the interview, especially direct comments about issues discussed

in writing were always regarded as more reliable.

In the case of teacher educators, the written curriculum for the teacher

education programme was used to confirm and to augment the understanding

attained through the individual cases. Similarly, as in the student cases, the

curriculum was analysed while producing the collective case description. The

aims and descriptions of study implementation were of special interest in

giving an alternative perspective on the contextual features. Descriptions of

the data based on the interviews and the curriculum were juxtaposed and in-

terpretation of the interview data was confirmed in this way.

8.4 Conclusion concerning the research procedure

The whole research process started with an interest that emerged from practi-

cal experience. Empirical notions helped to construct the overall view of the

research literature. The qualitative case study approach was intended to ad-

dress the need to understand the process of becoming a mathematics teacher

in the teacher education context. However, at the outset, it was clear that the

empirical and inductive approach would not be enough. Familiarisation with

the research literature was also needed to clarify the framework of teacher

education. This interplay between the theoretical and empirical perspectives

influenced the entire research process. Since the empirical procedure took

place alongside the theoretical construction, the research procedure cannot be

categorised as either inductive or deductive (Patton, 2002; Tuomi & Sara-

järvi, 2002; cf. Elo & Kyngäs, 2007).

Theoretical knowledge based on the review of teacher identity research

literature influenced the procedure at various turns. First, selection of the

cases, especially the need to cover both individual and contextual aspects of

teacher identity formation (Côté & Levine, 2002), proceeded from theoretical

understanding. The individual process could not been managed without con-

sidering the contextual features and socially shared conceptions of what a

mathematics teacher should be. The research context is thus described in de-


tail to justify the case selection and convey a sense of its features. Second, the

empirical procedure, especially the semi-structured interviews, was carried

out on the basic assumption that it is possible to investigate and interpret

one’s state of teacher identity through individual conceptualisations (Beijaard

et al., 2004). Consequently, only manifest content was of interest in the an-

alysis, not latent material (Elo & Kyngäs, 2007). Several interviews were

required to examine possible changes and reveal the on-going developmental

process. Each student case was elaborated separately, as an individual

bounded system, but the case displays are based on the shared conceptuali-

sation.

The overall research process took approximately four years (see Table 8).

By the time of the interviews with teacher educators, the first two rounds of

interviews with student participants had already taken place. The interplay

between empirical work and constructing the theoretical framework was es-

pecially significant for case displays and for the way multiple cases were

analysed.

114 Heidi Krzywacki

Table 8. The schedule of the research procedure

Time Research phase 2004 Autumn

Preliminary study

Data-gathering (student interviews)

becoming acquainted with the context and research literature

2005 Spring

Summer

Autumn

August–September

December

Analysing the preliminary study data

Preparation of the data-gathering (student interviews)

Constructing the research framework

Data-gathering

selection of research participants

student interviews (1st round)

Data-gathering and handling (transcription of the 1st interview)

student interviews (2nd

round)

2006 Spring

April–May

May

Summer

Autumn

Preparation of the data-gathering (teacher educators)

Constructing the theoretical framework

Data-gathering and handling (transcription)

student interviews (3rd

round)

teacher educator interviews

Reshaping the theoretical framework

Data handling (transcription) and analysis

2007 Spring–Summer

Autumn

Reviewing the research literature continues

Data analysis (the student cases)

Data analysis (the cases of teacher educators)

Writing the research report

2008 Spring–Summer

Autumn

Writing the descriptions of the case displays


2009 Spring



9 Teacher identity: formation through three cases

The process of teacher identity formation is examined here through two kinds

of case: two individual student cases, John and Mary, and the collective case

of teacher educators. First, the separate cases will be presented, and the three

research questions will then be answered in the last section, which concludes

the results.

Both student cases are treated as individual entities in order to highlight

the individual nature of formation of emerging teacher identity, since it is a

person who is involved with the process of becoming a teacher and who is

actually growing up to be a teacher. The three main theoretical themes under-

pinning the research questions are profiling the state of teacher identity

through characterisation, describing the interplay between the present image

of teacher identity and the image of the ideal teacher, and approaching iden-

tity formation as an on-going process.

In practice, the first research question regarding characterisation of

teacher identity is addressed through elaborating the developmental process

of the cases through cognitive and affective aspects of teacher identity. Fur-

thermore, emerging teacher identity is analysed through the subsets of the

present and ideal images, taking each aspect separately. Since changes that

may have occurred during the process were of particular interest, the second

research question regarding the present image of teacher identity and the im-

age of the ideal teacher is approached from the individual perspective. The

third question regarding the on-going process of emerging teacher identity is

addressed through the overall description of the individual developmental

process presented, in addition to the changes regarding the aspects on the

present and ideal levels. The background of the students and an outline of

their motivation as a prospective teacher are discussed first. Since the basic

information on these cases is described in more detail in the previous chapter,

the focus now is on the features likely to have influenced the developmental

process.

In addition to the individual perspective, the collective case of teacher

educators is to give an insight into the social perspective of teacher identity

formation and the contextual influences on the process of emerging teacher

identity. The image of the ideal teacher provided in the teacher education is

examined using the collective case display, which also addresses the research

questions regarding the ideal image and characterisation of teacher identity.

The collective view of the ideal mathematics teacher is seen in terms of the

individual aspects of teacher identity.

116 Heidi Krzywacki

9.1 Student 1: John

The first student case is John, who was the self-regulating student with moti-

vation for developing as a teacher. John was able to conceptualise his own

developmental process quite clearly, and had an equally clear picture of the

developmental process that he was ready to engage with. He considered prac-

tical experience as essential for his development because of the opportunity

to ‘witness’ oneself in the role of a mathematics teacher. His personal view of

being a good mathematics teacher was revealed as in conflict with that pro-

vided by teacher education.

9.1.1 Am I going to be a teacher?

The basis of becoming a teacher can be portrayed through three themes that

help to describe previous experiences and influential attitudes: a positive rela-

tionship with mathematics despite unpleasant school experiences, engage-

ment with self-development, and a relatively clear vision of how to become a

good mathematics teacher. First, especially at the beginning of the educa-

tional studies, John discussed the difficulty he had had in adjusting to the

school system during his school career. It seemed that, at least to some ex-

tent, the personal aims that he set for himself during teacher education em-

erged from his own experiences. His attitude towards mathematics as a

school subject had always been positive, despite his negative experiences.

His positive relationship with mathematics was not primarily based on being

extremely good at it; he considered himself talented but outperformance was

not something that would have been paramount.

It is mathematics that interests me and even if I did not always feel like studying it

well, I took care that I did somehow (at the time, I was going to be an engineer

with a university degree and I knew that mathematics was to be mastered in the

entrance examination). (portfolio, autumn 2005)

Furthermore, those negative experiences in learning mathematics emerged

from poor instruction. According to John, he was already able to distinguish

in elementary school between inappropriate feedback that caused bad feelings

and mathematics as a school subject. The first unpleasant experience was

about following instructions and inequitable consequences.

… The tasks were about algorithms and homework was to be done in the exercise

book. Instructions for the homework were that you were supposed to leave two

empty squares around every algorithm. The last task did not fit on the page, as

Teacher identity: formation through three cases 117

outlined in the instructions; I should’ve left two empty squares around it, but had

no space on the page to do so. So, I decided to save some space and I wrote the

task in a smaller space, resulting in having to do it again although it was correct.

I found this unreasonable, but fortunately I understood to focus my hate against

the unfairness of the teacher instead of the subject [mathematics].

(portfolio autumn, 2005)

Experiences in the school environment were based on the student’s own

schooling. John had not been a school teacher before taking teacher educa-

tion, and only had some experience in giving private lessons. Possibly, there-

fore, he built his own vision of good teaching and learning in mathematics

based on his school experiences at the beginning of the course, throughout

which the significance of having enough challenges as a learner and the

learner’s own active role were the key factors in good teaching and learning.

… I think it’s very motivating when kids can have a certain kind of existential ex-

perience in mathematics… for example, when you have an infinite unknown math-

ematical something, at least for me… those have been the kind of experiences I

have thought about, not during my time in school, but later (spring, 313)

Second, John seemed to hesitate over future plans for his teaching career.

After a brief experience in polytechnics and university physics as his major,

he ended up studying mathematics. John had also taken educational course

some years before out of curiosity. However, mathematics had always in-

spired him greatly, and mathematics mattered to him the most; the teaching

profession was only one occupational option amongst others.

H …well, could you say more in detail how you found your way into education,

why you decided to become a teacher?

S1 well I have several reasons; one is that I needed to make the decision about me

graduating, and I had already excluded the possibility that I could become a re-

searcher in mathematics, too old for it, and somehow it blew over… (autumn, 23)

I’ll act as a teacher as long as I keep learning what it is like to be a teacher and I

can familiarise myself with the school world… but I want to be a translator as

well… it provides some kind of certainty in my life that if this choice [of being a

teacher] is wrong for me as a future career, then I also have another option…

(autumn, 27)

Despite the uncertainty about this future occupation, John stated that he was

willing and suited to become a good mathematics teacher because of his

sociable personality and aptitude for working as a teacher.

118 Heidi Krzywacki

I think the most important reason for the choice of a career in teaching was that it

felt natural. I frequently reflect on how to teach or explain something… I think it’s

important to disseminate knowledge that is of the essence in some way. I believe

in the traditional ideal of civilisation and I regard natural science as a triumph of

the Western culture… I think that I have a strong aptitude for being a teacher. I

have many family members who are teachers and somehow I’ve grown up to be-

come a teacher. A profession is sometimes handed down. (portfolio, autumn)

Thirdly, in general, John could be portrayed as an independent and self-

directed student. He had a clear vision about being a good teacher as well as

how to become such a teacher already by the beginning of the educational

studies. He considered that there was not only one but multiple ways to act as

a teacher depending on one’s own personality. This principle paved the way

for him to become a mathematics teacher during his studies.

All teachers should teach in their own way, it is… you have to invent your own

way of thinking… but like I do… I think differently about these matters from how

they want us to think here [in teacher education], and how they teach us here…

(spring, 300)

Like many other students, John regarded being active in the developmental

process as meaningful. For him, the meaning of his own thinking and chal-

lenges in his studies were essential, including educational studies. Learning

university mathematics had been such an experience for him. He was opti-

mistic about teaching practice lessons because of the opportunity to take a

role as a teacher and to learn practical knowledge and skills, e.g., with the

help of video recording:

… it’s useful to see yourself on the video tape, then you notice if you have man-

nerisms, and it might broaden your mind to see yourself anyway. I think it was a

good idea to reflect on posing the questions… I did it rather well, I think the im-

plementation was alright… I also know whether I posed good questions or, for

some reason, not in the classroom, but then I might also miss something and it is

nice to notice… (December, 146)

9.1.2 The developmental process profiled through characterization

In John’s case, expertise in mathematical content knowledge was the founda-

tion of being a good mathematics teacher. In addition to mathematical com-

petence, he emphasised considering the student’s individual learning process

and the teacher’s support for it.


Mathematical content knowledge According to John, mathematical content knowledge is the basis for being a

good mathematics teacher in that the ideal teacher should be able to think like

a mathematician as well as possess expertise in mathematics. At the ideal

image level, the view of what was seen as valuable as a good mathematics

teacher neither changed substantially nor was widely reflected on. In general,

mathematical competence seems to be self-evidently crucial to being a good

mathematics teacher, who should be enthusiastic about mathematics and

should strive to improve mathematical competence when required.

… you should not teach something incorrectly… I haven’t thought of bringing this

up… of course you have to master the content in order to be able to teach it… I

think it is an ethical obligation; for example, that when a teacher is aware of

problems in mastering the subject that is to be taught, he should learn it first…

(autumn, 123–126)

One of the important aims [in mathematical studies] is to learn to think in a cer-

tain way, like a mathematician, so that when you have a mathematical problem

you know how to attack it like you should… then there is calculus, it’s good to

know that as well, but the most important thing is to learn the mindset …

(spring, 334)

After experiences in taking a role as a teacher in the first teaching practice,

John highlighted that a solid mathematical base is a tool for planning and

implementing lessons, as well as an aid in handling dynamic classroom situa-

tions. Since pupils have a right to rely on correctness in teaching, the

teacher’s knowledge should be mathematically exact and true.

… I think it’s about being ready to answer the questions if the topic is clear in

your mind, and essential issues you can decide on at the moment or… you can

choose as well… I think that knowing the subject… that you don’t get lost… the

content knowledge is then needed for being able to, well, to respond to questions

somehow and to come up with an answer… (December, 190–192)

It is essential from the viewpoint of professional ethics that you do no teach incor-

rectly or insufficiently, even if teaching well is more work than teaching insuffi-

ciently (portfolio)

John did not reflect on his own mathematical competence in detail during the

developmental process. According to the interviews and portfolio assessment

work, he found his own initial abilities good enough give him confidence.

John stated that his personal strength is his willingness to find out and to de-

velop his own mathematical knowledge when needed.

120 Heidi Krzywacki

H …well, how would you evaluate yourself as a prospective mathematics

teacher… what are your strengths?

S1 …well, probably that… that I have pretty well established mathematical con-

tent knowledge, that I… that I understand what it’s about. I regard it as rather

important, well maybe the most important accomplishment. (spring, 314)

In John’s case, the ideal and the present image of expertise in mathematical

content knowledge seemed to be closely connected, which consequently

showed a minimal gap between the ideal and his present state as a teacher

(see Table 9). John therefore did not have a real need for development in this

respect or for setting any further goals.

Table 9. The developmental process of mathematical content knowledge (John)

Autumn 2005 December 2005 Spring 2006

idea

l

Mathematical know-

ledge and skills are

seen as a solid base

for being a good

teacher. Pupils should

be able to rely on the

correctness of instruc-

tion.

Mathematical competence is the

basis for acting as a good teacher,

especially in handling dynamic

classroom situations. The teacher

is then able to focus on relevant

issues in teaching mathematics.

Besides, a teacher should be

enthusiastic about mathematics

and be capable of strengthening

his own knowledge base.

The basic idea remains

the same. Mathematical

knowledge is needed for

acting well in dynamic

classroom situations. A

good mathematics teach-

er is able to think like a

mathematician.

pres

ent

John does not discuss

his own mathematical

competence explicitly,

but he seems to be

confident about it.

Still seems not to be worried

about his own mathematical

competence. He states that his

strength is willingness to develop

his mathematical competence

further.

He feels that his own

content knowledge pro-

vides a solid base for

being a teacher.

Pedagogical content knowledge Expertise in pedagogical content knowledge was combined with the skill of

providing enjoyable and suitable learning opportunities in mathematics. Ac-

cording to John, learning mathematics takes place through one’s own active

thinking. Skills in posing mathematical tasks and mentoring pupils in their

own learning processes are relevant. It is the teacher’s responsibility to sup-

port this learning process by simplifying the central topics, and finding the

appropriate level of abstraction. A good teacher considers the individual

abilities of pupils carefully, is able to differentiate between pupils on this

basis, and provide challenges for gifted pupils.


You should be able to offer everyone some additional tasks for the good ones or

something intelligent to read about the topic, for example, something different

within mathematics that would develop skills or give them amazing insights…

something from advanced mathematics… (autumn, 78)

There are pupils, like, at different levels and I think the teacher owes those who

are more skilful... they have to be given the opportunity to learn, even if there are

others in the class who might miss something in the lesson...this would kind of

take into account the heterogeneity within the class... (December, 187)

Furthermore, a teacher needs to master the field of teaching and learning

mathematics in general and be able to highlight the most essential issues.

… what is essential in teaching… why in particular this exact topic is taught, why

this topic is included in the school course… if you do not master (the view of)

mathematics then it soon descends into learning idiotic algorithms, and well… it

means in percentage calculation many different kinds of formulas instead of re-

flecting the concept of the percentage and equations in mathematics books…

(December, 200)

In terms of the ideal image level, John first reflected on issues regarding the

viewpoint of the learner and the role of the teacher in the learning process. At

the end of the studies, John also specified his view of a good mathematics

education with three central aims: to gain basic calculation skills, to develop

mathematical thinking, and to apply mathematical knowledge in the real

world. In portfolio assessment work, John discussed the meaning of learning

objectives and essential values underlying the requirements for a good math-

ematics teacher:

It’s obvious that teaching objectives and ideals pave the way for the teaching

methods being used and at least some methods are being excluded based on these

objectives and ideals. If the aim is to guide a person towards self-regulated think-

ing, to direct them to apply knowledge and skills widely and to take others into

consideration, you cannot use drills or any method of conditioning, it’s not the

best way to achieve the aim… I consider that it’s important for them to have a

positive view of mathematics as a useful and clarifying tool for thinking, that you

don’t need to be afraid of or hate the subject, but that it is helpful for you in life,

study and at work. (portfolio, autumn)

John had doubts about his own competence in pedagogical content know-

ledge. He realised that he had no practical tools for implementing lessons in

the way he would like to, e.g., in achieving a good level of abstract in instruc-

122 Heidi Krzywacki

tion. It was challenging for him to make pupils see the beauty of mathematics

or to create positive learning situations.

I have wondered… that what kind of actual methods are there, and then I won-

dered how to evaluate and how to produce an exam and what kind of questions

there should be… if I was made to take a role as a teacher in the classroom, I

think those would be the issues that I’d hesitate the most to address…

(autumn, 36)

After the first teaching practice, he was able to set more detailed personal

aims. He considered creativity in planning the lessons as a special strength

for him.

I seem to come up with ideas very easily, that I have ideas for implementation and

for methods and I can implement a lesson that has good content… and certainty

for implementing the lesson, that I could carry it out the way I planned…

(December, 161)

In the end, despite the need for further development, John felt that he had

found his own way of teaching mathematics and reflected on his view of

mathematics teaching broadly.

… there are two stories side by side, a mathematical story like this and then the

story of calculus, which is necessary for understanding mathematics, to be able to

proceed one has to learn calculus… applications are needed as well… maybe we

have many stories side by side, which are followed. Calculus is needed for under-

standing the main story. (spring, 310)

Altogether, the image of the ideal teacher was reshaped gradually alongside

the developmental process without any major changes (see Table 10). Ac-

cording to John, a teacher is the one who is responsible for facilitating the

individual learning processes of different kinds of pupils. John reflected on

his present state as a teacher in terms of the ideal image, finding that further

development was needed in practical skills to be able to implement lessons as

intended. He seemed to have a clear notion of good teaching and learning

mathematics as well as of the skills required for implementing such teaching.

In this matter, the ideal image seemed to pave the way to become a better

mathematics teacher.


Table 10. The developmental process of pedagogical content knowledge (John)


idea

l

Mathematics should be

taught in a way that

everybody can under-

stand. Teaching math-

ematics is about

learner-centred matter;

differentiation and

taking care of learning

of all kinds of pupils.

Still, learners are seen to

have a central role in

teaching and learning

mathematics. A teacher

should help in this pro-

cess through simplifying

and bringing up central

issues. Learning math-

ematics should be active,

based on learners' exist-

ing skills.

A teacher should help students'

to learn and encourage pleasure

in mathematics. The main aims

of teaching mathematics are to

gain basic calculating skills, to

develop mathematical thinking

and to apply mathematical

knowledge in the real world. A

good teacher possesses an over-

all view of mathematics instruc-

tion.

pres

ent

John seems to lack

practical skills for

teaching mathematics

in classroom. He em-

phasises the signifi-

cance of finding a

proper level of abstrac-

tion.

He thinks that the chal-

lenge is not with cre-

ativeness or lack of

ideas. His practical skills

in implementing lessons

and considering students'

abilities need to be de-

veloped further. He feels

that he has found his own

way of teaching math-

ematics.

The most challenging thing in

teaching mathematics is to

mediate mathematical thinking

in the classroom and make

pupils see the beauty of math-

ematics.

Pedagogical knowledge and skills According to John, a good teacher should master general knowledge about

learners, learning, and teaching. Pupil-centeredness is the main theme in

teaching and learning, meaning that, in practice, a teacher has to consider the

skills of the pupils carefully. Solid pedagogical knowledge and skills are the

basis of being able to create a positive atmosphere in the classroom as well as

for differentiation.

If you consider these studies in education and how much you benefit from them…

but one should have at least a basic understanding of human psychology, about

the mechanisms of learning and memorising; there’s been quite a lot of research

on those topics, and there’s also good contemporary literature in Finnish

(December, 217)

At first, John did not explicitly mention the significance of practical skills.

With experience in teaching practice, practical skills and routines in class-

room management seemed to be more essential. He highlighted the import-

ance of classroom management in general for guiding learning according to

its goals.

124 Heidi Krzywacki

… well, the cognitive load should be focused on the topic that is being taught,

meaning that the load is not on if it is too difficult to do; for example, if it’s diffi-

cult to draw a table with four columns and fill the columns with something nice…

if it’s really difficult, then let’s not draw it but let’s use ready-made tables… well,

somehow the effort should be focused on the right issue… (spring, 321)

Besides, John talked about the importance of real interaction with pupils.

General pedagogical knowledge is also of help in this.

Well, respect for all pupils, this should be the basis for… and a certain kind of

honesty towards them and a willingness to meet them face to face, that I think is a

good basis for good instruction… (December, 185)

… it would be nice to have skills in human relations… to be able to manage the

situation without the need for strict discipline, that you are able to create this kind

of atmosphere in there [the classroom] (December, 226)

At the beginning of the educational studies, John has already realised his lack

of skill in managing the classroom as he would like. He was somewhat uncer-

tain about his authority in the eyes of the class, but judged his own skills in

social interaction with pupils as fine.

I could get started… well, I’m a bit scared of being in the classroom, as I have not

taught a whole class, I don’t think that any major problems will emerge but some-

how… how am I going to manage the situations and be able to recognise the right

things there, as all kind of things are going on all the time… (autumn, 91)

However, his view of his own competence changed slightly with practical

experience. Practical issues like giving instructions and implementing lessons

according to plan were better understood. He was aware of a need for further

development in mastering classroom situations in general. Particular skills,

like giving instructions, were emphasised but were associated particularly

with the role of the teacher in the classroom – how he would be able to use

all kinds of knowledge and skills in dynamic classroom situations.

… I should have guided activities in a more effective way, more directly and given

more precise instructions, to have concrete models… oral instructions are not en-

ough… I was too optimistic about oral instructions… a valuable lesson for me

(December, 152)

It’s really important to master routines as much as you can, for example, keep an

eye on the time despite the activity of teaching … it is extremely difficult at first,

well, at least I wasn’t able to keep things within schedule every time, when some-

thing took extremely long by accident… (spring, 356)


The image of the ideal teacher regarding general pedagogical knowledge did

not change much during the study year, but the overall picture was modified

towards dealing with practical skills (see Table 11). His views of his own

competence changed slightly. Before the first teaching experience, he could

conceptualise his strengths and weaknesses as a teacher. In actual practice,

skills in giving instructions and handling the classroom situations become

issues. He found understanding the pupils’ thinking and learning in the class-

room situations demanding. The gap between the present and the ideal image

was in fact quite substantial. The themes of concern were the same, but be-

cause of a high level of abstraction, and especially the lack of solid practical

experience, the ideal image of a teacher remained difficult of attainment and

self-evaluation was not comprehensive.

Table 11. The developmental process of pedagogical knowledge and skills (John)


idea

l

Since a teacher is re-

sponsible for pupils'

learning, one has to be

able to create a positive

atmosphere for studying

and learning, to motivate

and inspire as well as to

differentiate. Knowledge

and skills in ICT also are

needed.

A good teacher has pedagogi-

cal knowledge and skills in

general for classroom man-

agement. As learner-

centeredness is the key point

for him, skills in management,

e.g., giving instructions and

guiding pupils' work are im-

portant. A good teacher pos-

sesses general knowledge

about human beings and learn-

ing.

A good teacher under-

stands differences be-

tween people and their

learning processes. From

a practical viewpoint, a

teacher needs to have

routines and skills for

implementing lessons in

the way planned.

pres

ent

The willingness to un-

derstand and social

interaction with pupils is

his strength as a teacher.

He has some doubts

about own teacher auth-

ority due to being too

pally with pupils. Practi-

cal classroom skills need

to be improved.

John is surprised about the

level at which teaching and

learning should take place. He

recognises that he has to de-

velop his skills in instruction

and understanding pupils' basic

needs. A challenge is to im-

plement lessons in the way

planned, e.g., to keep to the

timetable and give clear in-

structions.

Despite the progress in

practical issues, he still

needs to develop him-

self. John feels that he is

able to understand pupils

better in general. Still, it

is difficult to evaluate

own competence with no

solid experience.

Thinking skills and competence for self-development According to John, a good teacher needs to be able to give reasons for deci-

sions made regarding teaching and learning. The starting-point is that there

are, as John maintained,

126 Heidi Krzywacki

…naturally, different kinds of good teachers, and it is of the essence that one is

able to act as a teacher in a way that is compatible with one’s own personality.

(portfolio)

At the beginning, he reflected on the importance of being capable of reason-

ing in order to strengthen his authority as a teacher in the eyes of parents.

To learn to give reasons for the choices somehow… if nothing else but to spice

your own talk… for example, if an angry mother gets in touch … you could spice

your talk by using terminology and you could calm her down that way [laugh]… a

teacher needs to be able to reason in different situations, it would be good to be

able to commit oneself among one’s colleagues (autumn, 50)

After the first six months, thinking skills were associated with development

as a teacher through analysing classroom actions. A teacher should have a

solid knowledge base for further development and to learn new things. Be-

sides, a teacher should be reflective by nature and capable of making peda-

gogical decisions within the wider context.

To be a teacher who reflects on his own actions and then is willing to talk about

his own teaching… what matters is the mindset, as there have always been good

teachers, and the quality of a teacher is not necessarily based on educational sci-

ences… it can be based on something else as well, but it’s essential to find a way

to think about the quality of a teacher this way, and only this promotes diversity,

everyone has to come up with it by themselves after all (spring, 342)

John did not reflect on his own background in thinking skills at all. He con-

sidered himself reflective by nature and capable of analysing own actions.

However, he did not understand the need for explicating his own thinking

process. It seems that becoming aware of the developmental process was nei-

ther necessary nor helpful in his opinion. The ideal and present image related

to thinking skills and the ability to develop oneself seemed to be removed

from each other. Altogether, the image of the ideal teacher did not pave the

way for him, even though he found the reflective stance meaningful in his

chosen occupation (see Table 12).

… a good teacher wants to do the job well by putting their own ideals into effect;

this leads on to striving to develop personal competence and teaching and this

way to observe how these features are implemented in teaching methods, and to

develop them when needed. (portfolio)


Table 12. The developmental process of thinking skills and competence for self-

development (John)


idea

l

A teacher has to be

able to give reasons

for his or her deci-

sion regarding teach-

ing and learning in

the classroom.

Development as a teacher is

possible through acting as one

and then analysing one’s actions.

A solid knowledge base is seen

as a good basis for further devel-

opment as a teacher.

As an autonomous profes-

sional, a teacher needs to

be reflective and analytic

about being a teacher.

pres

ent

John does not articu-

late this theme re-

garding his own

competences as a

teacher.

He considers himself reflective

by nature.

He considers himself

reflective by nature, but

John criticizes the need to

explicate his own devel-

opment and become

aware of it.

Affective aspects In addition to cognitive aspects, John reflected affective aspects associated

with being a mathematics teacher. Teachers should find their own personal

way to perform as a teacher, find a real interest in the teaching profession,

and engage with doing their best through a reflective and analytical approach.

John listed some features of a good teacher who is willing to do his best as a

teacher.

These constitute [all-round education and genuine willingness to perform well at

work] constitute a solid basis for professional ethics, from which, in my opinion,

ensue all essential distinguishing features of a good teacher, like objectivity, be-

ing stimulating, clarity, classroom management, receptiveness to criticism and so

on. A good teacher wants to do the job well and according to ideals… (portfolio)

John also emphasised the ethical perspective associated with the teaching

profession.

H well, why is it so important for a teacher to want to make pupils learn?

S1 It is about being genuine as well… a certain kind of getting to work and dedi-

cation are needed as a teacher, at least it makes it easier if you really want to…

do you want to do your job well and be good for the class, who are the ones learn-

ing? This can be reasoned in many ways, but one should be willing to do the job

well, and consequently should be willing to produce a good outcome

(December, 196)

However, despite a relatively clear view of the ideal teacher, the affective

aspect was not an essential part of his present image of himself as a teacher

(see Table 13). John mentioned that he is reflective and willing to learn new

128 Heidi Krzywacki

things by nature. He did not usually identify the requirements of the ideal

with his own developmental process as a teacher but rather with his role as a

university student.

Table 13. The developmental process of affective aspects (John)


idea

l

A good teacher is fair and equitable

towards the pupils, interested in

work and engaged in doing his best.

Still, being a teacher should be

according to personal characterist-

ics.

A good teacher is willing to

get to know the pupils and to

interact with them. Besides,

interest in their learning is

the most important.

Discussion on

this matter does

not take place.

pres

ent John discusses being able to master

his feelings. Besides, it is natural

for him to interact with other peo-

ple.

John regards reflectiveness

and willingness to develop

himself as his strengths.

No particular

statements

about the mat-

ter.

9.1.3 Identifying oneself with being a mathematics teacher

The overall view of the developmental process that John was involved in

during his teacher education is described here through three separate themes.

First, John emphasised the meaning of having practical experiences along

with his studies, especially taking a role as a teacher. Second, he felt a par-

ticular conflict between his developmental process and the contextual fea-

tures of the teacher education, especially regarding the ideal image provided

during the course. However, in the end, he still acquired the will to be a

teacher.

The significance of practical experience The significance of taking a role as a teacher emerged as essential in John’s

developmental process. At first, he seemed to feel competent and confident

enough to take a role as a teacher but, because of his lack of teaching experi-

ence, picturing himself as a real teacher was not possible. According to John,

practical experience leads to becoming a good teacher. One cannot learn how

to teach through observing; only some critical points can be grasped by ana-

lysing other people’s actions. It is not just acting as a teacher but also analys-

ing and evaluating the actions afterwards, as teaching practice showed him.

Everyone has to piece together their own picture, and it’s mainly through teach-

ing experiences and then through reflecting on actions during those experiences…

it’s been a really good thing (December, 167)


I don’t really know how I am as a teacher as I’ve been a teacher only for a very

short time (spring, 316)

At the beginning of the educational studies, he wanted to know more about

different methods and practical solutions and, even more essential, he was

willing to try them out to find the best for his way of teaching. Since he felt

that he had a lot to learn about practicalities in the classroom, he set particular

aims for the first teaching practice and for taking a role as a teacher.

The first aim is to conduct the lesson well enough. I wasn’t thinking about trying

anything new in the first lesson but to carry it out teacher controlled, concentrat-

ing on the topic itself. I’m planning to use inquiry as a method and try to get kids

interested, but the main focus is on carrying out the lesson itself. I believe that

having an uncomplicated lesson helps me best as an inexperienced teacher…

(portfolio)

After practical experience, personal aims became more detailed and related to

particular classroom situations for the succeeding teaching practice periods.

John came to see the significance of practical skills use generally. Further-

more, his expectations of pupils’ prior knowledge and skills became more

realistic, but otherwise, no great changes took place.

I’ve learned to be more realistic, for example, about what to expect in the class-

room and what the reality really is; for example, that you should be prepared for

unexpected, that some surprising issues can cause difficulty – this has been the

most important lesson for me… that you can prepare yourself for what works in

the classroom… (spring, 325)

At the end of his studies, he felt that he was about to find his way as a teacher

and be able to choose methods suitable for his own teaching style. His pre-

conceptions of teaching and learning mathematics had been strengthened and

it became clearer to him what kind of teacher he would like to be in the fu-

ture.

Well, applied teaching practice was pretty good… it helped me to start finding my

own style as a teacher, meaning how I’m going to act as a teacher, to be in the

classroom…then it is about building up the unique style you find and improving it,

and then about removing bad elements and replacing them with something that

works… it pretty often did feel like I found my own way of doing it (spring, 358)

Conflict with the ideal provided in the course Although personal aims and the vision of oneself as a mathematics teacher

became clearer during the educational studies, John originally had a relatively

130 Heidi Krzywacki

comprehensive vision of the ideal mathematics teacher and of how to become

such a teacher. Furthermore, he was motivated to develop himself. John

found the vision provided in the teacher education courses in conflict with his

own needs, so strongly that he wanted to avoid ‘inconvenient influences’.

S1 I have constantly kinda fought against achieving my aims, making the goals

into reality… well, kinda deliberately [laugh]…

H but has your thinking developed and have you found your own way?

S1 I think it has become clearer what I want… yeah, I do think it has been clari-

fied (spring, 343–344)

First, becoming a good teacher was in his opinion based on his own reflec-

tions and developing actions in the classroom. However, he did not consider

reflection or being explicit about the possible changes as a teacher helpful for

own development. Only activities focused on his own actions as a teacher

seemed productive.

And I don’t want to think about how my thinking has developed, for example… I

don’t see what purpose it serves, really… I have my way of thinking and it is im-

portant that I have my own kind of way of thinking and acting, it’s enough, it’s

constantly tested when facing reality and it either helps me survive or is useless

and then my way gets revised, it’s at the centre of self-reflection… but writing

about it as well? I don’t see the point… (spring, 368)

Second, the main idea was to find his own way of being a teacher and a

teaching style that was appropriate for him. However, because of his minimal

teaching experience, seeking and refining his personal teaching style was still

going on at the end of the course.

Well, I think that all teachers create their own way to be a teacher, their own

teaching style, however, in my opinion it is also important to be aware what is

happening around you and in the world… that would be/is useful…

(December, 212)

…when you act as a teacher on the basis of your personal abilities, you have to

make decisions and think… there’s no sense in making people think in a way that

doesn’t work for them… having different kinds of teachers is an advantage

(spring, 401)

In fact, he claimed that educational sciences were not the way for him to de-

velop himself as a teacher but practice and reflecting on his own actions –

becoming a teacher is something other than knowledge of educational theo-

ries. Furthermore, he found individual educational formulae useless because

of the lack of a broader framework in mathematics education. Only those


theories and formulae, which were related to his own development and inter-

ests as a teacher seemed useful.

I don’t want to underestimate educational research, it has clearly a point, but it

can’t be… fundamental to being a teacher, I think this kind of diversity should be

accepted, cherished, actually… if you emphasise educational sciences, for exam-

ple, then it leads those who don’t find it their own thing to sort of falling flat, that

you just have a job and you do it… it seems to be the only way, to act as a teacher

who thinks like an educational scientist… (spring, 304)

Even if he did not consider himself as a fully competent teacher and he

realised the need for further development, the course overall seemed irrel-

evant for his individual teacher identity formation. His rather strong precon-

ceptions of being a good teacher and high expectations for the course were

problematic. He needed to have time for his own reflections in order to inter-

nalise meaningful issues, and this was not addressed during the courses, in

his experience.

I would like to see how professor X produces an essay of five pages about a topic

that is not familiar to him in advance which should be based on the literature and

you have only five hours time; it can’t work if you want the essay to be a good

one… (December, 254)

The biggest problem was the conflict between his personal aims and the ideal

provided in the programme. However, he certainly considered mathematical

education at university meaningful.

Everyone has their own individual way of teaching , then you also have to create

your own way of thinking… but I seem to think differently about these issues from

how they think here or at least how they want to teach us to think (spring, 300)

…In my opinion, this highest possible instruction could be a little bit more open-

minded, to see the world in a different way… it’s also related to the whole issue of

being a teacher, not simply about the educational sciences and their way of think-

ing (spring, 406)

In the future At the end of the educational studies, almost at graduation, he said, ‘there is

no harm in being a qualified teacher besides other activities.’ Despite his

criticism of the course, he was willing to apply for a position as a teacher,

especially at high school and to continue the developmental process through

practical experience in a ‘real’ school environment.

132 Heidi Krzywacki

My viewpoint is that this teacher education cannot prevent me from becoming a

teacher, well… I think it was like it didn’t manage to spoil my willingness to be-

come a teacher… (spring, 346)

… I would like to be a teacher and develop a solid base of professional skills and

to qualify whilst working and then after a while I could rethink whether to con-

tinue or change my career or… but I am going to work as a teacher… I think this

is really… what I want to do but not necessarily for the rest of my life (spring,

420)

9.2 Student 2: Mary

The second case is Mary, who was a really motivated student and willing to

develop herself as a teacher. However, she was not particularly aware what

kind of mathematics teacher she was or would have liked to become. Mary

took an open-minded stance on her educational studies, which was to address

her needs as a prospective teacher. For Mary, teaching practice was the place

to witness herself as a teacher for the first time. Mary highlighted the import-

ance of the teacher’s authority in the classroom, the ability to direct different

kinds of pupils and to create a positive atmosphere. According to her, being a

mathematics teacher was more about genuine interaction in the classroom

than about the particular competences that a teacher should possess.

9.2.1 I am going to be a mathematics teacher

Mary’s point of departure as a prospective teacher may be described through

two themes, an affirmative stance towards schooling and commitment to a

developmental process as a student teacher. In general, school had been

something positive for her. She had adapted herself to the school system and

to being a student without difficulty. Mary did not recall any bad experiences

in studying and learning mathematics. It had always been pleasant but suffi-

ciently challenging. One reason she gave was that since she was not too tal-

ented in mathematics, she had benefited from school instruction.

It’s been a proper challenge, there have been tasks that really needed some think-

ing over, how to solve this, just at the right level of difficulty, but not so that it be-

came frustrating, not that I wouldn’t get it at all or understand it at all…

(autumn, 48)

No bad experiences come to my mind while I studied mathematics… therefore, it

provided me enough challenges, but did not overwhelm me. (portfolio)


Furthermore, she described mathematics lessons during her school days as

rather traditional without any ‘edutainment’. Later during her education

course, she paid attention to different methods and study arrangements that

she could use in teaching and learning mathematics.

In general, I’ve always liked mathematics and enjoyed the classes despite the fact

that my teachers had hardly used different teaching methods at all. Maybe my

classmates who weren’t so interested in mathematics would have expected to have

more stimulating activities. I was happy to have a teacher who mastered the topic

and who was truly enthusiastic about it. (essay about school memories, autumn)

The significance of authority as a teacher and relationship with pupils em-

erged in Mary’s reflections. She discussed her teachers with respect and

wondered how they managed to exercise authority over pupils and to create a

positive atmosphere in the classroom at the same time. She wondered

whether those teachers had a special secret. Despite the rather traditional

mathematics instruction, Mary had positive experiences in having an active

role as a learner while learning mathematics.

In general, Mary was motivated to become a mathematics teacher. Her

own schooling also seemed to be influential later in her teacher education.

She had no prior experience in school teaching but she had been involved

with free-time activities with youngsters.

I really feel that I want to be in the teaching profession. I want to inspire my pu-

pils to become enthusiastic about what has inspired me. It is naturally quite naive

to think that you could get the hopeless case in the classroom to be inspired and to

experience the joy of being successful. However, that is what I would like to as-

pire to do as a teacher. (portfolio)

She originally took mathematics at university just because of good marks at

high school. She had also considered the possibility of applying for the pri-

mary teacher education programme later after getting more additional points

for the application from school experience. It took her a year to realise that

her wish to become a teacher and her enjoyment of mathematics could be

combined. Before that, mathematics had represented an enjoyable interest for

her, whereas being a teacher was associated with having a real occupation.

In elementary school, I liked mathematics already and also dreamt about being a

teacher like many other girls. I just didn’t understand that I could merge these

two… I didn’t think of mathematics as a possible profession; it was just a hobby

and exercise to improve my thinking… However, during my first year I realised

that the teaching profession combines a great hobby, which means mathematics,

and a nice job, meaning being a teacher (portfolio)

134 Heidi Krzywacki

At the beginning of her educational studies, Mary was excited about having a

definite aim of becoming a teacher for the first time in her university studies.

In general, she was willing to develop herself as a teacher. She was relatively

receptive towards her studies, with an open mind, rather than expecting that

particular issues would be addressed. Her personal aims were not so clear and

in general she was willing to learn everything that was offered during the

year. It seemed that she expected that the image of the ideal mathematics

teacher would be clarified for her.

I haven’t really set any… but I try to soak up everything possible, well, like, a sort

of an attitude that this isn’t all that much, and you try and get as much out of it as

possible, and you concentrate all the time and so on… (autumn, 42)

She had particular expectations for supervised teaching practice, which was

her first opportunity to take a role as a teacher. Mary expected that, based on

the feedback, her view of herself as a teacher could be further elaborated.

I hope I can benefit from teaching practice as much as possible. Real teaching ex-

perience I don’t have… I have a sort of a feeling for teaching but, in reality, I

start from nothing. However, I want to get as much feedback as possible from my

mentors, in order to know what things I do well and what needs to be improved.

(porfolio)

As in discussion about school experiences, the idea of the teacher’s authority

and role in the classroom emerged in relation to personal aims. Mary con-

sidered her competence in handling all kinds of situations. She particularly

discussed the need to be able to master problematic situations that might arise

in the classroom.

How to act in different situations, that kind of thing I’d like to learn, to discuss

problematic situations and to go through how to handle certain situations… when

I heard horror stories from my friends, like ‛what would you do in this particular

situation as a teacher, when…’ …well, practical, different kinds of situations

(autumn, 27)

Before the first teaching practice and taking a role as a teacher in the class-

room, she emphasised her need to have a sense of herself as a teacher. It

seemed that she was both insecure about herself as a teacher and not aware of

her own image and competence in teaching at the beginning of her studies.

Only then it was possible to develop herself further.

Before the first teaching practice I have several thoughts about teaching and

learning, but the main idea here is to get some feeling and confidence for teach-


ing, as well as to gain some readiness for self-development and my own teaching.

(portfolio)

9.2.2 The developmental process profiled through characterization

For Mary, being a good mathematics teacher is founded on mathematical

knowledge that is something desirable but not a sufficient condition. She

highlighted the significance of pedagogical skills and ability in social interac-

tion with pupils in order to create a positive and encouraging learning envi-

ronment in the classroom.

Mathematical content knowledge In Mary’s opinion, mathematical content knowledge is a start in being a good

mathematics teacher but not something particularly essential. Before starting

her first teaching practice, Mary discussed the significance of mathematical

knowledge as a basis for clarity in teaching mathematics. Furthermore, the

ideal mathematics teacher is interested in and enthusiastic about mathematics.

… you have to be enthusiastic about it, and you also have to know the content well

enough in order to be able to present it clearly and don’t have to wonder how it

is… in other words, you need to be skilful and enthusiastic (autumn, 68)

After taking a role as a teacher during the first teaching practice, Mary dis-

cussed mathematical competence in new way. It became a tool for use in the

dynamic classroom situation and for making pedagogically good decisions in

the classroom. She saw it as the basis for providing well-structured instruc-

tion.

… if you think about the amount of mathematical education here, it’s probably too

much compared to what you will need as a teacher, but enough to understand the

mathematical background as well… it also clarifies your own mathematical basis,

and you know what’s being taught and where it all comes from (December, 166)

Furthermore, Mary associated mathematical content knowledge with being

confident as a teacher. For her, it was one way to strengthen authority by be-

ing able to answer unexpected questions. However, she was not sure whether

all university mathematics courses were actually needed and how well uni-

versity knowledge could be applied in school work.

136 Heidi Krzywacki

After going to a pretty deep level in mathematics, it’s somehow really clear in my

mind what is taught in upper secondary school, so then it must be quite useful,

even if I had wanted to study more things related to teaching, not so much just

‘hard’ mathematics… maybe I’ll gradually realise how useful it is

(December, 195)

Before teaching practice, Mary found her own mathematical content know-

ledge sufficient, at least according to her test results in mathematics courses.

Nevertheless, she had doubts about the adequacy of her mathematical compe-

tence for teaching, especially at the upper secondary school level.

…in upper secondary, if you happened to have somebody really intellectual, then

you might be near your own limit, you have to memorise the topic exactly, but… I

master the content required for lower secondary school, and some background,

and I’ve managed to get good grades here in all mathematics courses… Well, I

don’t really know how well I remember it all, but I could recap... (autumn, 99)

… subject matter knowledge seems to be, however… a little bit … I don’t know

about it… not sure how well I really know mathematics… (December, 183)

In teaching practice, mathematical competence was put to the test in the

classroom. Mary saw mathematical content knowledge as a basis for her self-

confidence as a teacher. At first, she seemed to be worried whether she was

able to create credible authority, but later she concluded that her mathemati-

cal competence was enough, at least in particular situations during the teach-

ing practice. She still seemed to suffer some lack of self-confidence. How-

ever, mathematical content knowledge was not something to be further de-

veloped in future.

There might be some situations, especially in upper secondary school, that you

might feel insecure about your expertise in the content… how it is and how to

avoid teaching the topic incorrectly, that you familiarise yourself with the subject

at hand before teaching, to ensure that you really master it, not just that you trust

your own expertise (spring, 293)

H What about your readiness as a teacher?

S2 Well, especially in mathematics, well… I have a feeling for it, I think I have it

under control… (spring, 373)

Altogether, mathematical content knowledge was not particularly essential

for being a teacher (see Table 14). Mary did not reflect on it more generally,

neither the ideal image nor the present image of a teacher. During her studies,

Mary became aware of the importance of mathematical content knowledge

for classroom actions and her self-confidence was strengthened in this regard.


However, the ideal image did not particularly pave the way for her develop-

ment.

Table 14. The developmental process of mathematical content knowledge (Mary)


idea

l

A teacher has to be enthu-

siastic about mathematics

and know the subject well

enough to teach clearly.

After the first teaching practice,

she connects mathematical know-

ledge with the dynamic classroom

situation and the teacher's ability

to make pedagogical decisions in

different situations. A clear pic-

ture of mathematics helps her to

be logical and clear.

Mary does not

particularly discuss

mathematical con-

tent knowledge in

detail.

pres

ent

Mary feels that her math-

ematical knowledge seems

to be all right, at least

according to her marks.

Still, some doubts emerge

about whether it is enough

for being a mathematics

teacher.

Mary regards her mathematical

competence as good enough, at

least in certain situations. The

level of knowledge is enough for

being a teacher, even if not the

best possible compared to other

students in mathematics.

She is satisfied with

her pre-knowledge

and skills in math-

ematics as a pros-

pective teacher.

Pedagogical content knowledge The relationship with pupils, especially the role of the teacher, proved rel-

evant to pedagogical content knowledge. Mary associated expertise in peda-

gogical content knowledge with being able to assist individual learning tra-

jectories. She considered that a good teacher is aware of the nature of math-

ematics learning processes, meaning that the cumulative nature of learning

mathematics needs to be taken into consideration. A teacher should thus be

able to follow the students’ learning process closely.

…to be the kind of teacher who could take into account how pupils really learn, so

that there would not be total lack of understanding, so one should observe how it

is going in the classroom, because mathematics is a bit like having to master the

previous piece of information and knowledge before learning anything new…

(autumn, 69)

Furthermore, different kinds of activities, like learning games and methods,

are the way to inspire poorly performing pupils to learn mathematics. Ac-

cording to Mary, it is the teacher’s responsibility to present mathematics ap-

propriately, to be clear and logical enough.

… for those pupils for whom it is not so easy, well if learning could take place

through some sort of a play, well I can’t think of any particular play at the mo-

138 Heidi Krzywacki

ment, but one could create something a little bit different and stimulating that

could be used in lessons… (autumn, 71)

… well, learning could take place in my lessons, so that I could teach so well that

pupils could understand it all and they would not need to wonder ’what did she

mean by that’… (autumn, 79)

After the first teaching practice period, in addition to clarity of instruction, a

good teacher has to have flexible teaching methods, which are the way to

motivate and create variety in teaching, to help as many pupils as possible to

learn and understand. Mary especially highlighted the importance of motiva-

tion and personal interest in studying and learning mathematics.

… when questions arise, then you could… if you have someone who just does not

understand/get it, you could create new ways to approach the topic, to be cre-

ative… I got one situation that was just like that… and I couldn’t figure any other

way to explain it… and for sure, there must be another way to approach it…

(December, 181)

… mathematics is like… in many schools, you need to motivate your class and so

on… many pupils are not necessarily able to relate mathematics to everyday life…

it is like ‛why do I need to study this… so much and this way?’… to know how to

motivate, skills for that (December, 169)

At the end of her studies, she also discussed expertise in school content and a

need for being aware of those issues related to specific learning tasks that

might be problematic. It was not only variety of methods which she con-

sidered an answer for supporting pupils, emphasising the importance of the

teacher’s role in presenting mathematics in a way designed to make learning

easier.

H Do you regard something as particularly important [in teaching mathematics]?

S2 to be aware of topics that are known to be difficult to understand or to realise,

how to represent the issues clearly, especially for those kids [with learning diffi-

culties]… to be clear enough (spring, 283)

Mary reflected on her own competence related to pedagogical content know-

ledge only after her first experience in the classroom. In her opinion, she

needed to improve her skills in delivery. Besides, at the end of the study year,

she realised that knowing several teaching and learning methods was not en-

ough. It was a challenge for her to implement different methods in the class-

room.

…well, I’ve noticed in myself that I’ve had to think it over, thoroughly, many

times, how to express certain things; what is the order and which words to use


when teaching a topic, the order of sentences in order to prevent a blurred flow of

information, when you just hope that pupils pick up the essentials and understand

it… how to concentrate on what and how to say things… when you have thought it

over the night before, you have an idea of how to carry it all out…

(December, 157–8)

In all, pedagogical content knowledge was not essential in her reflections on

being a teacher (see Table 15). At the ideal level, Mary highlighted the role

of the teacher in promoting learning. The ideal image was described in highly

abstract terms, and when Mary had no clear view of herself and her needs as

a prospective teacher in this phase of her career, the gap between these two

levels was considerable.

Table 15. The developmental process of pedagogical content knowledge (Mary)


idea

l

A good teacher has to be

aware of processes related to

learning mathematics and the

cumulative nature of the

discipline. Motivation

through various activities and

the teacher's responsibility for

presenting mathematics ap-

propriately are emphasised.

A teacher has to be clear and

logical, and make mathematics

easy for the pupils. Still, it is

the teacher's responsibility to

make mathematics accessible

to all pupils and to make them

understand through various

methods. Real life applications

and motivation are central.

Mary still emphas-

ises that a teacher

needs to support the

learning of her all

pupils through pre-

senting mathematics

appropriately.

pres

ent

Mary does not reflect on this

at all at the beginning of her

studies.

After teaching practice, she

recognises a need for devel-

opment in clear presentation.

It is not easy to

apply various meth-

ods in the class-

room, especially in

mathematics.

Pedagogical knowledge and skills Mary discussed the importance of pedagogical knowledge and skills to the

role a teacher has in the classroom. She stressed that a good teacher should

possess well-established authority in order to be able to provide a suitable

and positive learning environment for all pupils. A teacher should handle

classroom situations in such a way that an encouraging atmosphere and class-

room management could be purposefully combined.

Not too authoritarian, but to be someone who handles the situation overall, so

that there isn’t mayhem in the classroom or other problems with concentration or

something else… to be able to say in such situation that ‛hey, this is something

140 Heidi Krzywacki

that you should do…’ I want to avoid being too commanding, but I also want to be

able to sustain an interaction in the classroom all the time (December, 153)

After her experiences in the classroom, Mary also reflected on the importance

of mutual trust in interaction with pupils. She discussed how a teacher is able

to create confidential and unreserved interaction in classroom, which was

essential in creating a positive learning environment.

… to possess the skill of presenting topics in an understandable way, and also the

skill of noticing poorly performing pupils who have not necessarily understood or

are too afraid to ask, to be able to notice them… and for example, at the end of

the lesson when doing tasks individually, you can ask about other unclear issues,

then you don’t unintentionally humiliate them in front of the classroom

(December, 178)

At the end of her studies, however, Mary stated that teaching methods are

subject specific, a key to success in enhancing learning. However, the ideal

teacher thinks carefully about suitable methods and study arrangements with

different groups, and tries to take special needs into account.

I remember my teacher with fondness, he had the energy to invent new ideas… I

heard him think out loud that he was going to have a lesson, which he had thought

of implementing in a particular way, but that it wasn’t suitable for the group… it

makes me think that even if you teach the same topic but it’s not appropriate for

this particular group, then you conduct the lesson differently with another

group… it’s something that I want to hold on to… (spring, 304)

Mary, who did not have previous teaching experience, was anxious about her

authority as a teacher and about her ability to handle the dynamic situation in

the classroom at the beginning of her educational studies, when considering

her present state as a teacher.

… if I‘m going to be a teacher in secondary school, for example in X [the name of

area]… if I act there as a friend of the students, I’m worried about my authority in

their eyes; do I have it at all? It was easy there [in teaching practice school]

where everyone wanted to study, it was ok to be like a friend, but in the future, I

need to work on this problem… (December, 151)

After her first teaching experience, she elaborated on the issues associated

with teacher authority in more detail, paying attention to social interaction

with pupils, seemingly concerned about her ability to create authentic rela-

tionships with them particularly. However, feedback in teaching practice con-

firmed her view of herself as friendly and approachable. Being a teacher is


largely about one’s role in the eyes of pupils and the way of being able to

control interaction in the classroom.

I particularly hope that I can create an atmosphere in the classroom in which pu-

pils are happy and willing to learn. I think it’s particularly important to have a re-

laxed but still motivated mood in the classroom… In teaching practice periods,

my views have been confirmed… that I do well with youngsters and I earn their

trust without problems. (portfolio)

By the end of her course, she was more convinced about her readiness and

general skills for interaction with pupils, but still did not feel confident about

own authority in front of the class. Besides, her skills in organising classroom

situations so that all pupils could benefit much as possible were of concern.

She talked particularly about her ability to set limits on pupils’ behaviour and

giving signals about desirable actions.

… quite good feedback [in teaching practice], my other mentor in physics espe-

cially gave me very detailed feedback, about little things, and one thing was about

being like a mate to the pupils… someone was late and I had just said that it is all

right, welcome… assertiveness was needed, it matters if someone is late and if you

approve of it the pupils start coming in late, I think s/he was right about what s/he

said (spring, 295)

The pedagogical content knowledge aspect of the ideal image did not change

dramatically during her studies (see Table 16). Teacher authority and the

teacher’s role in facilitating learning for all were essential for Mary. After the

first teaching practice, she talked about clear delivery and practical tools in

the classroom. All in all, Mary reflected on her present state as a teacher re-

garding pedagogical content knowledge domain according to the themes in

her ideal image. The ideal image seemed to guide the developmental process,

even though the gap between the levels was considerable because of lack of

practical experience.

142 Heidi Krzywacki

Table 16. The developmental process of pedagogical knowledge and skills (Mary)


idea

l

According to Mary, a good

teacher is a rightful authority

to the pupils. A good teacher

handles different situations in

the classroom and is able to

create a positive and encour-

aging atmosphere. It is the

teacher’s responsibility to

promote learning for all.

A good teacher is able to

support everyone through

a positive atmosphere in

class and confidential

interaction. Still, Mary

emphasises the meaning of

authority and the role of

the teacher as facilitating

learning.

Mary emphasises skills

for authentic interaction

and a need to foster all

kinds of learners. A

teacher is responsible for

supporting learning

through clear presenta-

tion and motivation.

pres

ent

Mary reflects on whether she

has authority as a teacher

naturally and whether she is

able to handle classroom

management.

Authority and relationship

with pupils concerns her,

especially regarding class-

room management. Be-

sides, she wants to de-

velop her skills in delivery

in the classroom.

She feels that she is able

to construct authentic

relationships with pu-

pils, but building up a

suitable authority is still

an issue for her. Class-

room management is

something to which

Mary wants to pay atten-

tion.

Thinking skills and competence for self-development In Mary’s case, thinking skills and competence in developing oneself as a

teacher were not a relevant part of the process of becoming and being a

mathematics teacher (see Table 17). She neither associated thinking skills

with being a good mathematics teacher in terms of the ideal image nor related

to her image of herself as a teacher in different phases of her education.

Thinking skills were seen as helpful only when facing problems in school-

work and when trying to find her own way of teaching as an inexperienced

teacher.

I guess there will be such situations in practical school work… I have noticed that

I seem to reflect on situations afterwards; I think about how I should have acted

in a particular situation and I think it will also be like that in teaching… first, it is

about finding your own way of teaching and thinking like that, gradually you

learn… (autumn, 81)

When you teach something for the first time, it would be good to take notes about

things that pupils found difficult. It would be useful to take some notes for yourself

about lessons that you have given. How to explain something, how it was under-

stood, what was particularly difficult, what was successful, what I can improve on

for the next time, and so on. (portfolio)


Table 17. The developmental process of thinking skills and competence for self-

development (Mary)


idea

l Thinking skills are not seen as a relevant part of the image of the ideal mathematics

teacher. It is possible to find one’s own way of teaching through the systematic ap-

proach.

pres

ent Mary does not reflect on this at all during her educational studies.

Affective aspects Mary discussed affective aspects associated with being a good mathematics

teacher in terms of being approachable and fascination with the teaching oc-

cupation. A good teacher can be described through personal characteristics

like being approachable and skilful in social interaction with others. Mary

clarified her views through memories of her own school experiences and feel-

ings related to her own teachers.

well, to be a teacher that the kids would like, like being a mate in some way, like

being a big sister or someone who is approachable but… if I wanted them to listen

to me, then they would listen to me… (autumn, 79)

to be such an approachable person… and someone of whom pupils would not be

afraid to ask something… (December, 148)

In addition to appropriate personal characteristics, the ideal teacher should be

interested in being a teacher and willingness to find new ways to motivate

pupils. She talked about willingness to make mathematics understandable and

meaningful.

I would like to be enthusiastic… to have the energy to further develop and reflect

on all kinds of things that might be helpful to make pupils learn better… to inspire

them (autumn, 21)

To be enthusiastic about your job, firstly… and then to try to find some examples

that relate mathematics to their [the pupils’] lives, to have examples from every-

day life, which are easy to understand… mathematics is seen in everyday life, it

also exists outside school and is really useful and needed (December, 177)

At the end of the course, Mary highlighted that it was important not to expect

too much from oneself. No teacher is perfect, and this is good to remember

when trying to do one’s best as a teacher.

144 Heidi Krzywacki

Lastly, it’s good to remember that you cannot be perfect now no matter how hard

you try. You need to do your best but need to reserve yourself the right to have

some bad days as well. A teacher can’t blame herself for all learning or motiva-

tional difficulties that kids might have. Of course, you must try to do something

about them but you shouldn’t ask too much of yourself. You have to be lenient

with yourself and you need to endure possible failures. (portfolio)

In the first half of her educational studies, Mary had doubts about her charac-

teristics as a teacher. She reflected on her way of being a teacher, and

whether her personality was approachable and natural. The overall view of

herself and of her own authority as a teacher was discussed at length in all

interviews. Being approachable was not only an attribute of a teacher with

firm authority but also a premise for her in building her role as a teacher. By

the end of her studies, she seemed happy about her way of acting as a teacher.

H Talk about yourself as a prospective teacher, what are your strengths?

S2 my strength, but weakness at the same time, is that I know how to be a mate,

approachable … I have noticed that kids readily come and ask questions from me

and stay in the classroom after lessons to talk… I think I am approachable

(spring, 288)

Furthermore, Mary also regarded her attitude towards being a teacher and

willingness to do her best as her strengths. She talked about taking responsi-

bility as a teacher. However, by the end of her studies, she questioned her

ability to limit her workload. In this sense, her view of teaching occupation

had become somewhat more realistic.

A challenge for me is not to stick my neck out too much… to avoid being awake

all night thinking about the next day’s lessons… you should be able to impose lim-

its on that… (spring, 301)

Mary described the affective aspects associated with being a good teacher

through some desirable features, like being approachable, as well as her will-

ingness to do her best at work (see Table 18). Mary reflected on the affective

aspects regarding both present and designated states as a teacher through

similar ideas. It therefore seems that the gap between the two levels promoted

individual development.


Table 18. The developmental process of affective aspects (Mary)


idea

l

A good teacher makes contact

with pupils easily and is

approachable. Mary talked

about being enthusiastic

about teaching and develop-

ing one’s work.

A good teacher should be excited about being a teacher

and willing to develop new ideas for teaching and

learning mathematics.

pres

ent Mary considers herself as approachable and friendly.

Besides, she thinks that that her strength is willingness

to do her tasks well and take responsibility as a teacher.

After the teaching practice

periods, she reflects on

whether she is able to delimit

her duties as a teacher.

9.2.3 Identifying oneself with being a mathematics teacher

The overall view of the developmental process is approached through three

themes that emerged from the data: clarifying the view of being a mathemat-

ics teacher during the studies, identifying with being a teacher through practi-

cal experiences and plans for the future as a mathematics teacher in lower

secondary school.

Clarifying the view of being a mathematics teacher during the course The Mary’s incentive in attending educational studies was her willingness to

develop herself as a mathematics teacher. She had neither a clear vision of a

good mathematics teacher nor how to become one. During her mathematical

education, she had been missing a pedagogical viewpoint and, accordingly,

support for her personal development as a teacher. She expected that her

needs as a teacher were to be really addressed during the educational studies.

For her, studying university mathematics has not particularly been about be-

coming a teacher.

I’ve studied much more than I will ever need there [at school], but when you’ve

gone very deeply into… then it’s clear in your mind, including the topics that are

taught in upper secondary school, I think it’s useful… even if I feel that I would

rather have studied something more about teaching than pure university math-

ematics, but eventually I’ll see the benefit of it (December, 195)

With the educational studies, Mary seemed to build up her view both of her-

self as a teacher through practical experiences and of the ideal image of a

mathematics teacher. According to the interviews and additional written data,

146 Heidi Krzywacki

it seems that Mary expected to have a ready-made agenda for further devel-

opment during her studies, including setting general as well as personal aims.

In general, Mary took an open-minded view of her studies with no high ex-

pectations.

S2 Not really… nothing special, it was just to be open-minded to everything that’s

provided… I didn’t know how to prepare myself, there were no high expecta-

tions… I cannot say anything particular

H so, you have taken a receptive stance towards…

S2 yes, well.. nothing especially surprising springs to my mind

(December, 142–3)

Mary expected to obtain new ideas about being a teacher, especially math-

ematics.

… well, I’ve been receptive… well, I think about the whole year, it’s been some-

what of a surprise that there wasn’t so much new knowledge or amazing ideas

that I expected, it was more like something that you could figure out with common

sense… well, it’s been, well I did not expect it to be so, how to say, simple…

(spring, 271)

In general, Mary seemed to be satisfied with the vision of teaching and learn-

ing mathematics provided. However, once the vision of being a mathematics

teacher had been clarified in her mind during the studies, Mary talked about

some controversial issues that emerged. Firstly, she had difficulty internalis-

ing models for teaching and learning mathematics which were not accordant

with her conceptions of the ideal way of teaching. For example, she would

have wanted to take different learning styles into consideration.

… so to speak, it was different to what I would have done, it was ok but… I am

more like a ‛taking notes’ person and you need to have your own hands-on ac-

tivity; it’s then possible to check something from your own notebook… to memo-

rise how it was from there, rather than using the schoolbook… it [the notes] could

be in a shorter way and the essential issues already underlined in your notes

(spring 262)

Secondly, Mary found the idea of the ‛teacher as researcher’ in conflict with

her own idea of being a teacher. For her, producing an educational minor

thesis was not obviously necessary for a prospective teacher.

H well, why you need to do a minor educational thesis?

S2 I guess it’s about examining or something like that, that is the purpose, but I

think it’s somewhat … that you are acknowledged in one particular topic, a clear

picture of it, but if you have no intention of becoming a researcher it might be


somewhat frustrating, especially if you happen to have a topic that is not so inter-

esting… (spring, 363)

Thirdly, even if Mary did not have a clear picture of the best way to become a

teacher, she found the portfolio assessment work uncongenial. At the end of

her course, Mary associated the idea of a teacher who develops and changes

during a teaching career with her image of the ideal teacher. However, the

developmental process was not about systematic writing, and she did not

understand the significance of writing down one’s own reflections or of be-

coming aware of the process. For Mary, the developmental process as a

teacher was not something that should have been shared with others.

Portfolio assessment work is a good tool for stressing yourself out. I would reflect

on my lessons anyway because I want to become a good teacher. No doubt it

makes your reflection clearer when you have to write it down. But why would

anyone else need to know how I have developed and thought about issues? Teach-

ing practice has been the best part, however. I feel that I have certainly developed

as a teacher through that… (feedback questionnaire, autumn)

Taking a role as a teacher in practice Mary had high expectations of the teaching practice periods, during which

she was able to take a role as a mathematics teacher for the first time. For her,

becoming a teacher was strongly related to the practical experience of acting

as a teacher. At the beginning of her educational studies, Mary talked about

being a teacher so as to identify herself with being a teacher in the future.

However, she needed practical experience build up a clear image of herself as

a teacher as well as a notion of what kind of teacher she would like to be.

Mary had expectations for supervision during the teaching practice pe-

riods. She was willing to have guidelines for establishing aims, and detailed

feedback on her own performance as a teacher.

…well, like we have in small group activities, everyone has own turn to be in front

of the group and, of course, in teaching practice you have an opportunity to do it

on your own and then you get feedback… I think that the feedback itself is really

important; since you don’t necessarily understand that you are doing something

wrong or badly, it’s good to have someone to tell you about it (autumn, 116)

The first teaching practice period made the biggest difference. First, she was

able to describe her needs as a prospective teacher in more detail after it. For

example, she started to talk about the meaning of good classroom manage-

ment, which she noticed only during practice. Taken together, Mary high-

148 Heidi Krzywacki

lighted the role of pedagogical issues in teaching and learning mathematics

alongside mathematical competence.

I don’t remember any more what I said in autumn… well, I think I had more like

big thoughts in autumn, and now I might have more particular things, like how I

can explain this issue in more detail… something like clear performance, or how

to use the blackboard or how visible it’s at the back row and you should have

handwriting that‘s big enough, such little details… well, maybe because I had

only a little teaching experience, then I’ve noticed issues that also need to be con-

sidered when you teach (December, 160)

Second, the significance of mathematical competence acquired through

mathematical education had changed because of her practical experience. She

claimed that mathematical education had not been supportive in becoming a

teacher, and the previous developmental process had not really touched her

personally. However, the need for mathematical knowledge was seen from a

different perspective. Theoretical knowledge was also reflected in practice in

a new way.

… well, recommendation could be like, it would be useful to work as a substitute

teacher before starting the educational studies… I realised in the spring term af-

ter having experiences in basic teaching practice that I had something with which

the issues provided in lectures and small group meetings could be combined… I

felt I benefit more from these courses [spring term] than was the case in autumn…

(spring, 326)

Third, her view of the teaching profession expanded. She became aware of

features of the school context and of other tasks related to the profession.

well, I don’t know… a change if you can call it that, that I have realised that there

are so many other things, like supervision during school breaks, or if you have a

pupil with special needs which needs some extra things to be done… like HOJKS

[the personal study plan] in teaching practice in the field school… so largely

about those issues, keeping touch with parents and things that are not simply

about teaching… quite a lot is something else… (spring, 307)

Mary originally had doubts about her readiness for dynamic classroom situa-

tions. She became gradually more assured as a teacher, especially in her

social skills and mathematical competence as a secondary school teacher.

Feedback from supervisors in teaching practice was positive, sometimes too

positive, when compared with own view of herself.

…yes, it was somewhat funny because I did not regard myself… I was unsure of

myself when starting the first teaching practice, that I had no experience in teach-


ing and I thought that I’m not likely to be able to give really good lessons without

experience, then the feedback has been mainly positive… hmm, I don’t regard my-

self as really a good teacher and I surely have many things to be improved, but

maybe it’s just lack of time for thorough discussion and then only the major things

have been brought up, if you have not made a big mistake, then nothing about the

details… (spring, 297)

In the future Mary gained confidence in her willingness to become a teacher during the

educational studies, at the end of which she talked about herself ‛as a

teacher’. School experiences had strengthened her image of herself as a

teacher, and it seemed that she was sure of her career choice.

H …have you developed your own teaching style?

S2 yes, I have some kind of image of my style, I think it will develop further in real

work when you are a teacher every day of the week, after many hours of lesson it

will surely change, but I have a sort of vision of how I am as a teacher

(spring, 342)

Furthermore, she was able to imagine herself working in a school. Mary

brought up the need for implementing teaching in her own way, despite the

traditions at school.

Moving to a new work community of course needs readjustment, but it is import-

ant not to assimilate too much. I want to invent nice ideas for lessons, including

mathematics lessons that are traditionally run according to the same format. Even

if no other mathematics teacher in the school is interested in doing learning

games or inventing something else that isn’t according to the mould, I’ll try any-

way to bring something cheerful and hopefully inspiring and promote change in

order to motivate (portfolio)

Mary stated that she wants to work at the lower secondary school level be-

cause there she is able to find potential for ‘real’ interaction with pupils. With

younger pupils, education is not only about teaching and learning mathemat-

ics. She considered that being a teacher might be a demanding and labour-

some profession but she did not regard this as a special problem.

… well, I’m eager to start my work and especially to have those classes that I’ll

teach for a longer period… well, in lower secondary even longer than in upper

secondary school, however, to have the same group at least during the whole

course, you can create or hopefully you are able to create an atmosphere which is

nice to be in and that you could pay attention to every kid… well, I’m glad to start

working, I’m full of enthusiasm (spring, 348)

150 Heidi Krzywacki

9.3 The image of the ideal teacher provided during the teacher education

I now turn to the case description of the socially shared image of the ideal

mathematics teacher mediated in teacher education. The meaning of math-

ematical education as a starting-point for being a good mathematics teacher

emerged in the preliminary analysis of the collective view of teacher educa-

tors (Krzywacki-Vainio, 2008). The case display is based on two sources,

teacher educators’ views of the ideal image provided during the teacher edu-

cation programme and the written curriculum of the teacher education pro-

gramme. The idea in the case display is neither to concentrate on each teacher

educator nor separate sections of the programme individually but to construct

an overall picture of the ideal mathematics teacher, towards which student

teachers are guided. For the process of teacher identity formation, it is essen-

tial to understand the contextual features that may influence individuals dur-

ing the teacher education programme.

The socially shared image of the ideal mathematics teacher is elaborated

through two subsets: in general, and through characterisation of teacher iden-

tity. There are two reasons for this structure. First, the teacher education pro-

gramme is mainly constructed in accordance with teacher knowledge do-

mains. Only the subset of affective aspects associated with the teaching pro-

fession is additional to the sections of the programme. Second, it is possible

to juxtapose the perspectives of individual students with the socially shared

understanding of becoming and being a good mathematics teacher in elabo-

rating the collective perspective through the same subsets.

9.3.1 The general vision of the ideal mathematics teacher

The description of the ideal teacher starts with the general vision of a good

teacher mediated in the teacher education. Four common themes, which were

highlighted both in interviews with teacher educators and in the official cur-

riculum, emerged from the data. First, it was explicitly mentioned that a good

teacher is an expert in different knowledge domains, both mathematical con-

tent knowledge, and in pedagogical issues. For a mathematics secondary

teacher, it is especially important to gain the ability to think pedagogically

about teaching and learning mathematics. The basic domains of competence

were thus explicated even though it is possible to be a good mathematics

teacher in multiple ways.


… in my opinion, the division into three sections is quite good, to possess good

enough expertise in content knowledge that is the responsibility of the department

of mathematics, to have enough knowledge about learning, teaching and educa-

tion, methods and theories behind it that is on the responsibility of Sokla [the De-

partment of Applied Sciences of Education], and practical feeling for the teaching

profession is on the responsibility of the schools, in a nutshell… (TE5, 138)

In addition to expertise in various knowledge domains, the meaning of being

an educator, a pedagogue, was highlighted.

well… they would become teachers who are able to think, who master it. I think

I’m repeating myself but what else it could be than being an expert in teaching

one’s own subject, and at the same time being educators, like this when simpli-

fied… (TE2, 52)

Second, however, it is not only a matter of expertise in different knowledge

domains but also the ability to plan and implement instruction such that pu-

pils can learn. This principle refers to the student’s ability to apply know-

ledge in practice and to find the connection between theory and practice. In

the written curriculum, it is called ‘personal pedagogical theory that is ap-

plicable in practice’.

During the teacher education programme, a student teacher integrates content

knowledge, knowledge about education and different kinds of learners, pedagogi-

cal content knowledge, i.e., knowledge about teaching, studying and learning a

particular subject, and knowledge about school practices with each other as their

own practical pedagogical theory. The purpose of the programme is to support

the prospective teacher in becoming an expert in planning and implementing in-

struction, and in assessment and development. (curriculum)

Third, in addition to aspects of competence as a mathematics teacher, the

main aim is for all students to construct their individual way to act as a

teacher. The idea that there are multiple manifestations of a good teacher was

discussed, especially in the interviews with teacher educators. All students

should develop their own way of being a teacher based on their inclinations.

…well, in being a teacher and learning to teach, it is really important that you

find your own way to do it, it’s essential… everyone can become an excellent

teacher starting from personal characteristics, through different methods; I mean

that a teacher can act individually but still be excellent, you don’t need to imitate

anyone, just be yourself… (TE1, 163–4)

152 Heidi Krzywacki

Fourth, a good teacher possesses an inherent readiness for continuous profes-

sional development. During the pre-service teacher education, a student

should build up basic skills in self-development. According to the teacher

educators especially, the idea is not to assume that one can find a way of be-

ing a mathematics teacher immediately. It was more about formation of a

basic position as a teacher, becoming competent enough to take a role as a

teacher, and further development takes place in the future.

well, a teacher, I mean student teacher, should possess basic knowledge that en-

ables them to survive the first couple of years before they get more experience, it

makes them feel somewhat more confident of being there, that a student is not

afraid of going there… in front of the classroom and facing pupils… (TE10, 97)

… well, to have a readiness which is a good basis for acting as a teacher, at least

in some way, and then they could develop it in future, continuously… (TE6, 136)

The comparison between the views of teacher educators and the written cur-

riculum reveals one main difference worth highlighting. Since the written

curriculum sees the school system as a part of society, a teacher is seen as

someone who should promote the idea of active citizenship, social equality,

and understand multiculturalism.

During teacher education, the emphasis is on active citizenship, societal equality,

and mutual understanding between cultural values. (curriculum)

However, the teacher educators did not discuss issues of the societal perspec-

tive in general. Only the teacher educator who is responsible for the special

course on societal and cultural issues addressed this issue.

9.3.2 The characterisation of the ideal mathematics teacher

The image of the ideal mathematics teacher mediated by the teacher educa-

tors is conceptualised through cognitive and affective aspects. Basically, al-

though the separate theoretical courses during teacher education are to ad-

dress the various competences that a good teacher should possess, affective

aspects of the teaching profession emerge during various courses. The overall

picture of a good teacher is complex and there are great strains on being a

good teacher.

[demands for a good teacher] … well, it is a really large area when we talk about

pedagogical skills and of course, we have various courses for that, maybe too

many courses, like ‛pajatso’; one message in my lectures is that this is not some-


thing that a single person could really master, so many demands that need to be

met, it is not possible for the individual (TE11, 42)

Mathematical content knowledge Mathematical knowledge was regarded as the basis for being a mathematics

teacher. A good teacher possesses solid knowledge in different mathematical

topics. All teacher educators unequivocally shared this view. However, defin-

ing the essence of mathematical knowledge was somewhat problematic and

not possible to define in one way only.

well, when talking about the knowledge that is needed, of course you have to have

enough knowledge of mathematics, and that is attained during the courses… an-

alysis, meaning differential and integral mathematics quite a lot, well then of

course algebra, you really need to master that… geometry, the amount of that has

decreased, but altogether… that is basically what we have included in basic

bachelor level courses; those you need to master (TE4, 19–24)

However, discrete pieces of mathematical knowledge are not enough. Exper-

tise in mathematical knowledge is more than competence in its separate parts

as it requires understanding the nature of mathematics as a discipline. A good

teacher has constructed an overall view of mathematics, which is needed for

providing the fundamentals at school.

One has to construct a more coherent and accurate view of mathematics, defining

the separate pieces. Teaching is localised, piece by piece, but a teacher should be

able to integrate the pieces into a broader mathematical context. It’s not always

successful as integration should take place in the students’ mind. It’s a matter of

learning, not teaching. (TE4, 36)

Furthermore, mathematical thinking and ability in mathematical argument

were also included in the skills that a mathematics teacher should master.

Although only cognitive aspects are discussed in the written curriculum,

affective aspects related to mathematics as a discipline were brought up by

the teacher educators. A good teacher should be truly interested in mathemat-

ics as a discipline and feel that the school subject is something special per-

sonally.

But as a secondary school teacher you also need to have a special relationship

with and interest in your own subject, a kind of special enthusiasm about it

(TE8, 12)

154 Heidi Krzywacki

Pedagogical content knowledge The significance of pedagogical content knowledge became apparent in vari-

ous ways. However, some central themes emerged from the interviews and

the written curriculum, despite the different approaches to teaching and learn-

ing this particular school subject. First, a good teacher was seen as a profes-

sional with ability in pedagogical thinking who is able for example to plan,

implement, and assess teaching and learning in mathematics. Furthermore, a

teacher should understand the special features of teaching and learning math-

ematics, like being aware of methods appropriate for this particular school

subject.

H Could you describe in more detail what you mean by ‛teaching skills [didaktiset

taidot]’?

TE8 well, these are mainly about methods used in practical teaching situations,

but then also the ability to plan and assess particularly in one’s own subject, spe-

cial skills for that might differ from other subjects (TE8, 13)

Teacher educators mentioned the need to find a new approach to teaching and

learning mathematics. A good teacher is able to implement this in different

ways to those used during their own school time. Associated with this desir-

able change, a mathematics teacher is seen as someone who, for example,

pays attention and is willing to promote the individual learning process

through interaction with peers.

… my aim is no more than I could say trying to provoke ‛disturbance’ in our stu-

dents’ thinking, in their heads, so that they would start to wonder how this math-

ematics should be taught, that it would not be simply in accordance with their

own school experiences, how I was taught, and I think this ‛disturbance’ could be

something like, as we said earlier, to think of other possible ways to teach, also

using discussions in the classroom… (TE10, 57)

Furthermore, a good teacher finds the interface between university mathemat-

ics and what is included in school mathematics. The importance of math-

ematical education is related to the teacher’s ability for pedagogical thinking,

especially whether a teacher is able to apply mathematical content knowledge

meaningfully in the classroom or not.

Surprisingly, content knowledge is not good enough, no coherent view on math-

ematics… some students do not even master content which is taught in high

school. It is not problematic for classroom management or acting as a teacher in

front of the classroom but for finding the central idea. Content knowledge might

be fragmented. (TE5, 130–132)


A good teacher is able to simplify the mathematical content so that pupils can

understand the essentials. Therefore, a teacher should have an overall image

of school mathematics in addition to mathematical content knowledge.

… about dropping some learning material, it is something… you need to know

mathematics well enough to understand that authors of school books put every-

thing in the book that they know about the topic, to be able to understand what is

not really essential (TE5, 51)

However, when presenting mathematical content in simplified format, a

teacher needs to be careful to avoid inaccuracy and incorrect transformation.

For example, a good teacher pays attention to the correctness of mathematical

writing on the blackboard.

Only with the help of the overall picture is a teacher able to present math-

ematics appropriately. For this, a good teacher needs a solid mathematical

and educational knowledge base. The role of a good teacher should be as a

promoter instead of a lecturer in the classroom. Actually, most of the teacher

educators emphasised the importance of understanding mathematics from the

viewpoint of the pupils. Only then is a good teacher able to promote individ-

ual learning processes.

…if a secondary school teacher is only interested in his or her own subject, it is

not enough. Real interest in pupils is also needed, meaning that the other half of

the truth is about the ability to interact socially with children and youngsters, to

be interested in their lives, try to find the boundaries between one’s school subject

and presenting the subject… (TE11, 13)

A need to motivate pupils and recognise the affective aspects associated with

mathematics emerges, especially in learning mathematics. According to the

teacher educators, a good teacher is aware of potentially negative aspects of

learning mathematics and, furthermore, tries to identify with pupils’ learning

problems.

[a good teacher] motivates pupils to be active and think for themselves, doesn’t

try to make him/herself irreplaceable and somehow tries to make pupils like

mathematics and work on mathematics, because basically the only way to learn it

is to do it yourself; but to motivate and inspire… You can do it in many ways…

the important thing is to do it. (TE5, 23)

Second, all secondary teachers should understand the unique characteristics

of their subject, in this case mathematics. For example, it is necessary to

understand the cumulative nature of mathematical knowledge and the conse-

quences of this for teaching and learning.

156 Heidi Krzywacki

You need to create mathematical understanding on the basis of previous know-

ledge, you cannot start in the middle and start to build up something that is under-

standable… mathematics as a subject is so different [compared earlier with his-

tory], you can repair the wholes somehow, but you need to start again to build up

an overall picture (TE10, 34)

Furthermore, mathematics was also seen as a special school subject because

of its nature as an exact science and the need for accuracy in classroom teach-

ing. The mathematical language used in instruction paves the way for pupils’

learning processes.

… a certain kind of logic and consistency in how teaching is carried out, maybe it

is more important than in teaching languages… teaching mathematics is not only

about learning algorithms, but also teaching how to think… in order to do this,

teaching thinking as well as algorithms, you need to be meticulous and organised

(TE5, 24)

Third, a good teacher is acquainted with the curriculum process at different

levels and is able to share the responsibility for curriculum work in school. A

teacher should thus understand the wider societal importance of mathematics

as a school subject. However, this viewpoint was underlined in the written

curriculum, not particularly emphasised by the teacher educators.

A student gets to know the societal tasks of school instruction. A student gets to

know curriculum work at different levels, to know the national framework curricu-

lum, and planning by those responsible for teacher education… A student has the

ability to make pedagogical decisions that are reasonable and conscious for cur-

riculum work and cooperative planning at school and for the school subject. A

student will attain readiness to using ICT in instruction in diverse ways…

(curriculum)

Pedagogical knowledge and skills Pedagogical knowledge was discussed through two thematic subsets, theo-

retical and practical knowledge. A good teacher was seen as someone, who is

aware of different aspects of the teaching and learning process in general and

who is capable of applying such knowledge in the classroom.

All teachers should master the same, starting from trivial issues like those de-

scribed in the Clarke’s model, to master content knowledge, instruction skills, a

wider educational view combined with teaching skills, and first of all, respect for

pupils… not everyone can be a mathematician but each pupil is valuable and it is

a teacher’s responsibility to help them to gain the best possible outcome in the

subject… to be educator-teacher-motivator in contrast to a scornful embarrasser

(TE2, 15)


A good teacher fully understands the pedagogical issues. During the theoreti-

cal educational courses, basic knowledge is divided into four main fields,

which a good teacher should master. A good teacher is also acquainted with

different kinds of learners and special needs in learning, especially in math-

ematics.

The basis of teaching should not be going through learning materials but the

learning of pupils; planning the instruction should start from their viewpoint, and

from observations and theoretical knowledge that a teacher has… in order to

make an improvement, this should be the ground… (TE5, 50)

First, a good teacher should possess knowledge about the learning process

and the basis of developmental psychology. Only then is a teacher able to

support the developmental process of both individuals and groups. The con-

structivist view of education for enhancing individual learning was widely

mediated during the teacher education.

Actually, issues related to education… about development and education, they

were essential, well… particularly, to understand what kind of developmental

phases there are, those were really needed and important… (TE7, 127)

Second, a teacher should possess knowledge about special education, for ex-

ample, about learning and behavioural difficulties that might appear in the

classroom. A good teacher should also know how to perceive learning and

behavioural problems in teaching situations.

If a teacher has no clue what kind of divergent individuals there are and how you

could help and educate them, take them into account in instruction, then you get

scared, meaning that teachers are scared of difficult pupils, really, and especially

how to present mathematics… to make pupils understand is really heavy stuff

(TE1, 22)

Furthermore, according to the teacher educator who was responsible for the

course in special education, a good teacher is open-minded about special

needs education in secondary school teaching, and in order to attain this aim,

some students need to change their attitudes.

well, it is really important in studying special education to change attitudes,

probably the most important, only after that, distribution and receiving know-

ledge… (TE1, 122)

Third, the ideal mathematics teacher is acquainted with societal and institu-

tional issues relating to the school system. In practice, this means that a

158 Heidi Krzywacki

teacher should be able to be analytic about education and be able to discuss it

from historical, societal, and philosophical viewpoints. Furthermore, know-

ing the historical background of the existing school system makes it possible

to understand the overall picture.

In a nutshell, to show the existence of the historical structure of the school, con-

troversial tendencies that test the system, behind the tendencies there are ideolo-

gies and values, and then to show the relationship between the society and school,

how school has an effect on society in the long run, especially…and this double

binding, meaning that at the same time school should convey cultural heritage

and should pave the way for the future in continuously changing circumstances…

(TE11, 55)

The need to be acquainted with multiculturalism emerged only from the cur-

riculum.

A student should get to know the philosophical and institutional background of

education and the educational system as well as essential educational policy is-

sues… The challenges of a multicultural society and the role of the school in civil

activity should be paid attention to. A student should have the ability to under-

stand and analyse education and educational systems from the historical, societal,

and cultural viewpoint as well as to handle multiculturalism. (curriculum)

Fourth, a good mathematics teacher is familiar with educational research,

especially on mathematics education. This includes both research knowledge

about teaching and learning mathematics as well as basic knowledge of re-

search methodology.

In addition to knowing about basic educational issues, a good teacher is

able to apply this to teaching, studying and learning process. In practice, for

example, this means that a good teacher uses flexible teaching methods in

suitable ways and practical work skills in the classroom. Besides, a teacher is

able to identify problematic situations and to handle them in an appropriate

way.

… there are no similar days or similar situations, one has a bad day and the other

has a good one… one should have eye for observing the situations (TE10, 28)

Furthermore, a good teacher has skills in using information and communica-

tion technology in his or her teaching. However, this was particularly in-

cluded among the essential qualities of a good teacher by the educators.

Last, a good teacher possesses skills in interaction, and furthermore, is

aware of his or her own personal interactional features. This is not only re-


lated to interaction with the class but also willingness to cooperate in plan-

ning and decision-making regarding the curriculum work at school.

I think it’s one of the basic skills that a teacher should possess, not being a tradi-

tional teacher who shuts the door behind her and in the classroom, implements

teaching freely autonomously… to cooperate with others… (TE10, 69)

Thinking skills and competence for self-development A good teacher masters basic research skills and understands the main princi-

ples of educational research. Students traditionally produce a small-scale the-

sis on educational issues in their major subject. It may recently have also

taken the form of a pedagogical project and reflections on it. Associated with

this kind of work, a prospective teacher should become skilful in writing re-

search with a solid structure.

A student gets to know research on teaching and learning the subject, and pro-

duces independently either their own minor thesis or a pedagogical product de-

signed for the learning situation. A student develops the willingness to be an ex-

pert who does research on and develops his or her own work. A student is ready

for life-long learning and further studies in educational. (curriculum)

The main idea here is that a good teacher learns how to reflect on his or her

own work systematically and generally is able to examine and develop it. The

idea of a teacher as researcher is thus internalised as a part of being a teacher.

For example, good teachers are able to strengthen their own expertise in vari-

ous aspects when needed.

… to give some skills for reflections about teaching and learning, before entering

school work, also to provide skills in analysing one’s own teaching and what kind

of instruction promotes understanding and what does not, to get to know different

ways to teach and learn, different options that one can try… (TE5, 66)

During teacher education, the aim is to extend competence in taking a role as

an autonomous professional who is responsible for planning, implementation,

and assessment of teaching and learning. The ability to reason in pedagogical

decision-making is one of the main objectives in the teacher education pro-

gramme.

There is a lot of discussion about the quality of Finnish teacher education; it

means that a teacher should think independently, which is the reason why I do not

want to provide knowledge as such… it needs to be reasoned and even then, I

keep saying that there is no one to check you in the back of the classroom, you

have to do what is the best in your opinion (TE9, 33)

160 Heidi Krzywacki

One reason for the need to be an autonomous professional is the idea of de-

veloping a personal way as a teacher based on individual inclinations. Since

there is no one kind of ideal teacher nor shared norms on how to implement

teaching and learning in the classroom, a good teacher needs to be an inde-

pendent professional.

… it is a philosophical approach to bring up challenging underlying questions,

without having ready-made answers… well, everyone needs to find the answers,

whether this way or that way, there is no… you cannot decide only one way, those

are questions of values, almost everything in school (TE11, 86)

During teacher education, in addition to educational research activities, criti-

cal reflection on societal and philosophical issues related to education are

seen as essential for a professional teacher. Furthermore, portfolio assessment

work also aims at skills in personal reflection and the ability to conceptualise

the developmental process. According to the curriculum text, portfolio as-

sessment work should be a tool for combining different knowledge domains

with practical experience and for reflecting on one’s personal educational

philosophy.

A student sets personal aims and reflects on his or her own actions critically. S/he

reflects on strengths and weaknesses based on experiences and received feedback.

Portfolio assessment work helps a student to integrate pedagogical content know-

ledge and practical experiences gained through teaching practice together. Port-

folio work promotes building up a personal educational philosophy…

(curriculum)

Affective aspects Affective aspects associated with the image of the ideal teacher fall into two

categories, the personal characteristics of a good mathematics teacher and

attitudes towards the teaching profession. This viewpoint cannot normally be

derived from the official written curriculum. However, in the interviews with

teacher educators, several conceptions of the desirable characteristics of a

good teacher were shared. The affective aspects were especially discussed by

supervisors at the university schools.

Personal features of the ideal teacher

In the interviews with teacher educators, various issues regarding the appro-

priate characteristics of a teacher arose. The message seemed to be that a

teacher should be suited to the teaching profession but this may involve dif-

ferent characteristics. For example, a good teacher should be emphatic and

capable of taking professional responsibility.


… of course, a good teacher is… rather emphatic than cold-hearted, rather re-

sponsible than careless; a teacher is unique and sufficiently creative, the other

pole is being mechanical, like a stereotype… (TE2, 79)

Furthermore, a teacher who is well organised is able to handle practical situa-

tions. However, this is something that people can learn.

… of course, you need to be organised in order to handle your own life as well as

your role as a teacher … maybe people become teachers who can do this, you can

also improve in such issues if needed… it is not necessarily so important in all oc-

cupations (TE4, 52)

According to some teacher educators, it is easier to list undesirable personal

traits than the image of a desirable personality. No teacher should have psy-

chological problems. The entrance examination seemed to be important in

reducing so-called undesirable personalities.

I would say that it’s not possible for everyone to become a teacher; of course, a

person with normal intelligence can build up a knowledge base, but a teacher

needs to have a strong psyche… if you happen to have mental problems…

(TE1, 141)

Actually, it is not possible for just anyone to become a good teacher.

… those might pass the entrance examination, even if we interview in order to

have only motivated individuals… those who are not suited to teaching, it’s rather

like leave those who are obviously not suitable and direct them somewhere else…

(TE8, 68)

… there are some personal features that you cannot gain by sitting in school, you

can probably improve some features but there are others that you either have or

not (TE4, 20)

The teacher’s role in the classroom was also discussed. A good teacher is one

who takes the role as an educator and paves the way for the pupils to learn.

This is possible with good social skills, which are needed both in the class-

room as well as in parental and collegial cooperation. It is not only about

social interaction and constructing authority with pupils but also about taking

a role as a professional in the eyes of other adults.

well, I think that a good teacher is the one who says what to do, after all, well…

we can discuss authority or something else, but it has to be the teacher who has it

in the classroom and who has to create this atmosphere in the classroom…

(TE10, 29)

162 Heidi Krzywacki

A good teacher is encouraging and fair to all pupils. Neither gender issues

nor success in mathematics should influence the relationships between the

teacher and the pupils.

Especially in comprehensive school, to be equal and fair, not to discriminate or

play favourites… those are skills that we discussed with student teachers, what

are the problems in using discrimination based on gender, girls and boys, in the

class. It is not necessarily always bad, but what kind of dangerous values remain

hidden… (TE5, 49)

Furthermore, a good teacher is self-confident in his or her own teaching abil-

ity. Mathematical competence can be a solid base for developing the

authority needed in the classroom. However, knowledge and skills are valu-

able only when combined with sufficient self-confidence as a teacher.

Content knowledge and skills are not the main point but self-confidence, trusting

oneself. If one is self-confident overwhelming content knowledge and skills are not

needed. However, expertise in subject matter may enhance self-confidence.

(TE11, 16)

Attitudes towards being a teacher

In addition to certain personal characteristics, the teacher educators shared

the idea of engagement with the teaching profession. First, a good mathemat-

ics teacher is well-motivated and committed to being a teacher in general.

If students are motivated to become teachers… It’s not about external motives but

willingness to develop as a teacher and then it is possible to direct the process

during teacher education. (TE7, 154)

It’s personality that is the starting-point for everything, and this field is not for a

person with no fervour, you need to have a real fervour (TE6, 153)

Furthermore, a good teacher values the teaching profession in general.

… basic skills in teaching, how to plan and face pupils and so on, and then to cre-

ate a positive attitude towards the meaning of the teaching occupation

(TE2, 53)

One of the main ideas in the teacher education programme is to promote the

teacher’s willingness for self-development. A good teacher seeks new ap-

proaches and pedagogical ideas that s/he could apply in the classroom.

But you can develop – I notice that myself as well, that I have developed, meaning

that there are opportunities to do things differently and you can always improve

your expertise in content knowledge, there are no limits… technical solutions, us-


using different methods, teaching methods, new technology has also appeared…

great potential if you are willing, but you need to have the willingness… to be en-

thusiastic (TE11, 52)

The state of a good teacher is continuously reshaped. In the interviews as

well as in the written curriculum, the vision of a good teacher includes the

idea of a professional who is willing to take a critical stance towards his or

her own teaching and the educational system in order to develop it further.

There is always another way to do things.

… well, teachers should be innovative and should also be… critical of one’s work,

…not afraid to renew your way of teaching and to try different solutions… well,

promoting this attitude in prospective teachers is rather important… (TE1, 162)

The willingness for self-development includes the idea that a good teacher is

capable of becoming aware of the limitations of his or her own competence.

… a teacher who thinks he or she knows the topic under discussion and is not

willing to go through it again, is a fool… (TE7, 29)

9.4 Conclusions concerning the cases

The process of teacher identity formation was approached through the two

kinds of case described in the previous sections. The overall view and sum-

mary of these cases is given according to the three research questions based

on the underlying theoretical themes originally outlined.

Instrumental case study like this concentrates primarily on the phenom-

enon itself, the overall process of teacher identity formation rather than sepa-

rate cases as bounded systems (Stake, 1995 and 2005). However, the devel-

opmental process may be examined only through individuals and their under-

standing. The starting-point in this research has been that identity is an indi-

vidualised entity, meaning that there is a person to identify with being a

teacher (see Korthagen, 2004). The process of identity formation was thus

approached through two separate student cases, those of Mary and John. In

addition to these, the collective case based on the views of teacher educators

was used to understand the contextual influences and the social reality in

which individual development takes place (e.g., Assaf, 2008; Goos, 2005; see

also Wenger, 1998). The summing up follows the themes of the research

questions, both by viewing the cases separately and, in Miles and Huber-

man’s terms (1994), by comparison between the cases in order to extrapolate

164 Heidi Krzywacki

the results to a more general level. The idea is not only to juxtapose the stu-

dent cases, for example, focusing on the profile of the developmental process,

but also to contrast the individual cases with the collective view of the ideal

image of being a mathematics teacher.

9.4.1 Characterisation of teacher identity

The first research question was related to characterisation of teacher profes-

sional identity, i.e., how is teacher identity profiled through its cognitive and

affective aspects. In general, characterisation makes it possible to see teacher

identity both in individual and social terms. The nature of the individual iden-

tity of a mathematics teacher may be seen through a range of cognitive and

affective characteristics, as with John and Mary. Furthermore, it is possible to

examine the interplay between an individual and the context according to

particular features associated with being a professional mathematics teacher

(Arnon & Reichel, 2007).

In John’s case, mathematical knowledge and skills formed a solid base for

acting as a professional mathematics teacher. It was self-evident to him that

being a good mathematics teacher requires mathematical competence. John

seemed to have a cognitive approach. He highlighted the need for under-

standing and supporting the learning process of individual pupils, for which a

teacher should possess expertise in pedagogical content knowledge as well as

general pedagogical knowledge and skills. For him, mathematics was some-

thing that needs to be presented to pupils in an appropriate way, for example,

by highlighting its special features as a discipline. Furthermore, a teacher

should take responsibility for making learning accessible to all. John associ-

ated thinking skills with being a teacher because of the need for further de-

velopment. The developmental process conceptualised by John was strongly

profiled through the cognitive aspects of actions as a teacher in the class-

room.

In Mary’s case, social skills and affective aspects were important in the

teacher identity profile. According to her, a teacher needs mathematical

knowledge and skills to be able to act professionally. Mathematics should be

presented in a suitable way, and a good mathematics teacher needs to be able

to motivate and use various teaching methods. Mary did not associate think-

ing skills with being a mathematics teacher. However, she regarded reflective

activities as a way of envisioning her own way of being a teacher during her

studies. Mary paid great attention to the relationship between teacher and

pupils, for example, the teacher’s authority in the classroom. In Mary’s case,


individual teacher identity was associated with an educator who takes respon-

sibility for the overall learning process, and who is able to create an appropri-

ate atmosphere in the classroom. Mary highlighted the significance of per-

sonal characteristics like being approachable.

John and Mary reveal how characteristics associated with being a math-

ematics teacher enable one to profile individual development and teacher

identity in particular, highlighting different characteristics as essential to

teacher identity. For example, mathematical content knowledge seemed to be

basic to being a mathematics teacher for both of them, but they put different

stress on this. John highlighted this expertise as fundamental, whereas Mary

considered it as desirable. For Mary, affective aspects and skills in social

interaction were crucial. In addition to differing emphasis on particular char-

acteristics, the range of features associated with teacher identity might differ

as well. In the cases of Mary and John, subsets of thinking skills and affective

aspects were not automatically included in the profile as a professional

teacher. Expertise in educational research and the idea of ‘teacher as re-

searcher’ especially was associated with teacher identity by neither.

Similar to the characterisation of individual teacher identity, the socially

shared idea of a good mathematics teacher and societal positioning may be

approached through a range of cognitive and affective characteristics. The

case of the teacher educators represents the collective view of a good math-

ematics teacher that is mediated during teacher education. In terms of the

image of the ideal teacher, conceptualisation of different features makes jux-

taposing of individual and social views possible, which is elaborated in more

detail in the following section.

9.4.2 Approaching teacher identity through the present and ideal images

The second research question was about exploring teacher identity formation

through the present image of teacher identity and the image of the ideal

teacher. From the individual perspective, identification with being a math-

ematics teacher takes place at two levels, through the image of one’s present

state as a teacher and through the image of the ideal teacher, which is con-

sidered as a range of desirable and valuable characteristics as a mathematics

teacher (Arnon & Reichel, 2007; see also Sfard & Prusak, 2005). The case

displays of John and Mary have been described within this framework. First,

the individual image of the ideal mathematics teacher is gradually reshaped

by experience. At the beginning of his course, John had a relatively clear

166 Heidi Krzywacki

vision of being a mathematics teacher. Nonetheless, some changes took place

during his studies. For example, practical classroom management skills were

incorporated into the ideal image after personal experience in the classroom.

Mary was different, as her overall view of the ideal mathematics teacher was

less clear. Her approach was to be open-minded with the vision provided by

teacher education. She did not conceptualise her image of the ideal teacher

regarding all aspects in detail. Furthermore, her image was highly abstract

and general, involving, for example, reflections on pedagogical content

knowledge. However, the image of the ideal teacher gradually became clearer

for her and she was able to envision herself more precisely by the end of her

studies.

Second, the image of the ideal teacher comprises a range of features asso-

ciated with being a good mathematics teacher, which are combined with per-

sonal development with differing emphasis. A student should be able to im-

agine him- or herself as a teacher in the future and to identify, at least partly,

with the image of the ideal teacher as a personal guideline (Virta, 2002; see

also Arnon & Reichel, 2007). For example, affective aspects as a teacher

were somewhat disconnected in John’s developmental process. John reflected

on affective aspects generally but he did not identify with these in his reflec-

tions on his present state as a mathematics teacher. However, in his case, ex-

pertise in both mathematical content knowledge and pedagogical content

knowledge was closely related to the developmental process. In Mary’s case,

pedagogical content knowledge played a relatively important role in the ideal

image. However, even though conceptualisation at the ideal level took place,

the gap between the ideal and present image shows that she had difficulty in

identifying herself with the ideal in this respect.

Third, the gap between the ideal and present image of teacher identity is

relevant for the individual developmental process. The width of the gap be-

tween the two levels is significant (Sfard & Prusak, 2005). The ideal image

directs the developmental process if it is something achievable from the pres-

ent state. John described the vision of pedagogical knowledge and the skills

that a good mathematics teacher should master in highly abstract terms. At

the same time, his view of his present competence was in closely related to

his practical teaching skills. His personal goals thus seemed to be distant

from the ideal image. However, his ideal and present images of mathematical

competence seemed to be closely connected. John did not have a real need

for development in this respect, no need to set any further goals. For Mary,

affective aspects at the ideal level were in accordance with reflections on her

present state as a teacher, which involved the same themes as were associated

with the ideal image. Altogether, it seems that the ideal image paves the way


for reflection on one’s present state as well as for setting personal aims for a

developmental process inconsistently, depending on the aspect.

Fourth, individual developmental processes for students take place within

the context of teacher education. The collective case of the teacher educators

is one way to make the socially shared image of a mathematics teacher ob-

servable and may be juxtaposed with individual images of the ideal teacher.

The overall notion of the ideal teacher was conceptualised according to the

structure and the main principles of the teacher education programme. In

general, the views of the teacher educators were parallel with the written cur-

riculum, except for some issues like the societal position of a teacher, which

was greatly emphasised in the written curriculum but not particularly brought

up in the interviews with the teacher educators. Generally speaking, the

socially shared perspective was cognitively emphasised. However, the affec-

tive aspect emerged when the teacher educators discussed the desirable per-

sonal features of a mathematics teacher considered in the entrance examin-

ation. We may note that even though the teacher educators responsible for the

programme implementation represent separate perspectives, there was no

fundamental disagreement (cf. Korthagen, 2004).

In the case descriptions, the interplay between individual processes and

the context appears in terms of the ideal image, although differences between

the individual and socially shared image as such are not of interest here. After

all, the empirical part of this research was based on only a few cases. How-

ever, the cases of individual students appear in a new way when contrasted

with the socially shared image of the ideal teacher provided during teacher

education. An individual gets to know about this shared ideal image through

interaction with others (see, e.g., Walshaw, 2004). The social environment

paves the way for individual development, for example, through providing

activities and teaching experience, where the individual view of the direction

of developmental process is parallel with the shared visions (see Younger et

al., 2004). In Mary’s case, the interplay between social and individual images

took place without any major controversy. Mary adopted an open-minded

stance towards her course, and was therefore willing to internalise the vision

provided. However, she emphasised some issues differently from the socially

shared image of the ideal teacher, including the ability to promote learning

and to create a positive and encouraging atmosphere in the classroom. Only

by the end of her studies, when her own view of being a mathematics teacher

had been clarified, did some controversial issues emerge, for example, re-

garding her vision of ‛the teacher as researcher’. John’s case was different

from Mary’s. John was an example of a self-regulated student with a rela-

tively clear image of the ideal mathematics teacher. In his case, the interplay

168 Heidi Krzywacki

between social and individual viewpoints was approachable, especially

through controversial issues.

Both students considered the domains of teacher knowledge as a basis for

professionalism in accordance with the academic vision provided at the uni-

versity. The collective case of teacher educators was structured according to

the individual disciplines that each educator represented. Unsurprisingly,

mathematical content knowledge was crucial to the image of the ideal teacher

both in individual and socially shared ideal images (cf. Hodgen & Askew,

2007). Expertise in mathematics was not something about particular content

but more like a mindset that a mathematics teacher should possess, recalling

the findings of Ferrini-Mundy et al. (2007). Pedagogical content knowledge

was similarly associated with a good mathematics teacher. The main idea was

to be able to present mathematics positively and appropriately in order to

enhance individual learning. Of course, individual students emphasised

somewhat different aspects of the way to do this. For example, Mary invested

more energy in considering affective aspects in classroom implementation.

Moreover, a different emphasis on the general pedagogical knowledge and

skills emerged. For the teacher educators, pedagogical knowledge was com-

posed of academic content that was only partly included in individual ideal

images. First, the societal perspective on the teacher’s role and competence

for tasks outside the classroom were missing in the students’ conceptualisa-

tions. This is understandable because of limited practical experience as a

teacher. Mary and John discussed pedagogical competence as closely associ-

ated with classroom activities and the ability to enhance learning mathemat-

ics. Furthermore, John challenged the meaning of educational science for a

professional teacher and discussed controversial issues that he had confronted

in his teacher education.

In the light of these cases, thinking skills and the ability for reflective

practice seemed a problematic part of the ideal image provided in the teacher

education. Both Mary and John were willing to undergo self-development

through reflecting on their present readiness as a teacher. However, the idea

of systematic examination of one’s actions or making these reflections acces-

sible to others were not seen essential for a good teacher. Furthermore, know-

ledge about research methodology and the ability to produce educational re-

search were not seen as a relevant part of professionality (cf. Gitlin et al.,

1999). Despite their critical stances, the vision of a teacher who is able to act

as an autonomous professional and to make pedagogically reasonable deci-

sions in the classroom was internalised by both students. Willingness for fur-

ther development and engagement with the teaching profession in particular

were seen in as essential to professionality.


9.4.3 The on-going process of teacher identity

The third research question, what is the formation of emerging teacher iden-

tity like from the viewpoint of change, was related to the on-going process of

teacher identity formation The focus of the student cases has been on the de-

velopmental process through which an individual becomes a teacher (Kortha-

gen, 2004; see also Côté & Levine, 2002). The case displays of John and

Mary are structured to highlight the changes that may take place during the

process in forms of the characteristics of teacher identity and the levels of the

present and ideal images. For example, the view that John had of himself as a

teacher with skills in classroom management and practical pedagogical issues

was clarified. For him, social interaction in the school environment, not sim-

ply the possibility to take a role as a teacher but also the feedback in teaching

practice, promoted the changes in his views (cf. Danielewicz, 2001). He be-

came more aware of his needs for further development and it seems that the

change took place in two respects – by becoming aware of his own present

image as a teacher and by clarifying the ideal image seen as desirable. In ad-

dition to the clarification of the present and the ideal images, the changes also

take place in characteristics and the way an individual stresses each of them.

For example, Mary seemed to change her view of the role that expertise in

mathematical content knowledge had in her teacher identity. During her

studies, she associated the need to possess solid mathematical knowledge

with the ability to act as a good teacher, and stress was put particularly on

affective features and social skills.

The on-going developmental process of teacher identity formation cannot

be scrutinised in depth simply by external interpretation of possible changes

at three separate data-gathering points (Richardson & Placier, 2001). The

process of becoming a professional teacher is also examined here through

self-reflections that the students explicated in the interviews and in supple-

mentary written products. Since internalising one’s role as a teacher and con-

verting this role into one’s own professional identity was of particular inter-

est, assumptions and engagement in the developmental process as well as the

degree of internalisation of the vision of a good mathematics teacher pro-

vided were discussed in the case displays. Naturally, the motivational back-

ground of a student plays an important role in the developmental process

(e.g., Virta, 2002; Younger et al., 2004). Both John and Mary were willing to

become and to imagine themselves as mathematics teachers. It seems that the

personal developmental process can be conceptualised in two ways, not only

through separate characteristics that can be conceptualised in terms of the

present and ideal images, but also through the overall state of teacher identity

170 Heidi Krzywacki

associated with the personal feeling of professional identity. In practice,

Mary and John constructed their view of professionality as teachers and be-

came aware of own understanding about the characteristics by which they

define a professional teacher. Besides, both students gradually began to feel

like a real teacher (cf. Korthagen, 2004; Walkington, 2005). These cases are

examples of different ways to become and to act as a professional mathemat-

ics teacher. Mary was convinced of her commitment at the outset, and study

provided activities through which she became assured of her choice of future

occupation. For John, the change towards having the feeling of being a ‘real’

teacher took place to some extent and, according to his reflections, the devel-

opmental process was to continue in his position as a teacher in a ‘real’

school environment.

Last, the idea of continuous self-development was included both in indi-

vidual and socially shared views of teacher identity. During teacher educa-

tion, the main objective seemed to be attaining readiness for further reflection

and development, which takes place in the school environment through social

interaction with pupils and other people involved with schooling. One of the

main ideas according to teacher educators was to learn self-reflection and to

take a critical stance towards one’s own state as a teacher. Students did not

find this academic way to conceptualise their development and to share it

with others useful in their personal process (see Walkington, 2005). How-

ever, both the students and the educators shared the idea that becoming a

teacher in its all aspects is not the underlying objective of teacher education.

The essential idea is to start and to promote the developmental process that

an individual will be involved in in the teaching profession.


10 On the trustworthiness of the research

The traditional evaluation criteria for reliability and validity of the study de-

sign and methods used in quantitative research cannot be applied to this

qualitative case study because of its different paradigmatic basis (see Lincoln

& Guba, 1985; Miles & Huberman, 1994; Stake, 1995). As Bassey (1999)

remarks, checking external validity in a case study is problematic. For exam-

ple, the cases under examination, like John and Mary, were not selected for

their potential to be representative examples of all possible students but for

their potential to give some insight into the ‘typical’ process of becoming a

mathematics teacher during teacher education. Therefore, trustworthiness

needs to be elaborated through criteria appropriate for the premises of the

qualitative case study approach and for the particular purpose of this re-

search.

The trustworthiness of qualitative research can be evaluated on various

ranges of criteria (Patton, 2002; Tuomi & Sarajärvi, 2002). Patton (2002)

states that the quality of a study with a pragmatic starting-point is to be

judged by its intended purpose, available resources, and the procedures fol-

lowed. Besides, more than meeting the requirements of each criterion of

trustworthiness, the quality of the research is dependent on the coherence of

the research procedure overall (Tuomi & Sarajärvi, 2002). In practice, the

quality of the research report is essential for scrutinising the procedure that

has been carried out. Since the issues of trustworthiness should have been

brought up throughout in reporting the case, this chapter is to highlight some

essential notions that have actually already been reported. In order to address

the requirements, this research report includes discussion about the subject

and the purpose of the research, elaboration of the researcher’s engagements,

selection of the cases, the relationship between the researcher and research

participants, the research schedule, details of the analysis process, and va-

lidity regarding such things as ethical issues (Tuomi & Sarajärvi, 2002).

The modified range of criteria for evaluating trustworthiness is used in

order to take into consideration the nature of case study research. Trust-

worthiness of the research is examined by elaborating credibility, transfera-

bility, dependability, and confirmability (Tuomi & Sarajärvi, 2002; see also

Miles & Huberman, 1994; Patton, 2002). The questions about confirmability

of the role of the researcher have already been discussed in the chapter on the

case study approach, which examines its influence on the research process

because of different engagements and position in the research context. In

addition to these matters, triangulation has been added as a fifth issue par-

172 Heidi Krzywacki

ticular to case study research (see Patton 2002; Stake, 1995; cf. Yin, 2003).

These five categories are related to each other and partly overlap, but still

comprise a comprehensive basis for discussion.

10.1 Triangulation

The aim of triangulation is to cover different perspectives in order to attain

fairness during the research procedure and diminish misunderstandings of the

nature of the case (Patton 2002; Stake, 2005). The question is about whether

the research subject or cases are interpreted properly and in accordance with

‘reality’, here in accordance with intersubjectivity. To do that, the study de-

sign, data resources and data analysis should enable capturing the nature of

the case. The aim is not only to capture something directly visible and ex-

plicit but also to identify tacit features and to try to understand them (Miles &

Huberman, 1994; see also Lincoln & Guba, 1985). In this research, the pro-

cess of teacher identity formation has been approached through the perspec-

tives of teacher educators and students in order to reveal its multiple aspects.

There are several ways to carry out triangulation in case study research, as

Stake (1995) discusses based on the work by Denzin (1989). First, data

source triangulation examines the phenomenon of interest in different times

and situations to see whether it manifests itself in the same way. The re-

searcher observations are to be considered in different circumstances when

the phenomenon is explored through several sources. This research uses

mainly the data from semi-structured interviews with the students and teacher

educators since teacher identity and its formation is seen as approachable

through conceptualised understandings. Even if direct observations in the

classroom were one way to get information about situational manifestations

of teacher identity at the personal identity level (Côté & Levine, 2002; see

also Gee, 2000), it would not have informed us about the formation of emer-

ging teacher identity without meanings given to the experiences taking place

in social interaction. While experiences promote the on-going process of

identity formation, as a series of changes, the interpretation of the appearance

of teacher identity could not have been done only by an outsider, but with the

students who had experienced the classroom situation as a teacher and whose

understanding is of interest. Furthermore, because the opportunities for actual

classroom experience are limited during the teacher education programme

and the observation data would have covered separate situations only, the

semi-structured interviews were to address the purpose of the research best.

After all, the students reflected on their practical experiences in the inter-

On the trustworthiness of the research 173

views, and with this arrangement, the interviews were not overly concen-

trated on separate experiences but on the overall understanding of the state as

a teacher and the developmental process in general.

In addition to the interviews with two kinds of research participant, writ-

ten documents, the feedback questionnaires, and the official curriculum of the

teacher education programme were used to augment the main data. The over-

all idea was to build up research data that would reveal different perspectives

in accordance with the theoretical framework; for example, approaching the

developmental process both from individual and contextual perspectives. The

selection of research participants, especially the teacher educators, was in-

tended to reveal multiple perspectives within this particular study pro-

gramme.

Second, methodological triangulation took place only in augmenting the

interview data with direct observations on written documents. In practice,

both interview data and documents were elaborated through content analysis.

However, since the structure of the written documents was also used for en-

hancing the researcher’s understanding, direct observations were a part of the

data analysis process. The structure of the teacher education programme was

particularly taken into consideration. Besides, observations of the context

also helped to build up a picture of the contextual features that influence in-

dividual teacher identity formation.

Third, neither theory triangulation nor investigator triangulation, which

Miles and Huberman (1994) call a critical friend, was used in this research.

The overall aim was to build up a framework for the theoretical approach and

use case study for empirical examination. The analysis and research proced-

ure has thus taken place only within one theoretical framework. Furthermore,

investigator triangulation usually takes place in cooperative research projects

in order to enhance the quality of drawing and verifying the conclusions. The

research procedure here has been carried out alongside cooperation between

various university partners for developing the teacher education programme.

Some ideas have been presented to the teacher educators, who have com-

mented and made critical observations in joint seminars. Even if no other

person has gone deeply into the analysis, cooperation with teacher educators

and student members in the joint seminars has promoted the researcher’s

understanding of the phenomenon.

Furthermore, member checking is the way to have critical observations

and interpretations as a source of data, and to help the researcher to triangu-

late her own observations and interpretations (Stake, 2000; see also Lincoln

& Guba, 1985; Patton, 2002; Yin, 2003). In this research, member checking

was used when research participants were asked to review the case descrip-

174 Heidi Krzywacki

tions for accuracy and palatability. Both the teacher educators and the stu-

dents who are represented in the report received drafts beforehand to show

them how they were to be presented and interpreted. Member checking was

not only to verify the case displays but also to ensure mutual understanding

of ethical issues such as protecting anonymity of the research participants.

Member checking involved no major changes, but the researcher’s interpreta-

tion was strengthened.

10.2 Credibility

Credibility is about whether the phenomenon has been interpreted adequately

and with authenticity on the basis of the research data. Miles and Huberman

(1994) claim that the question in qualitative study is not about correspond-

ence between the findings and the real world, but about whether the findings

make sense and whether they are credible for the participants and the readers.

In this research, as mentioned in the paradigmatic background, the data is

based on different experiences within the teacher education programme con-

ceptualised by the research participants. Intersubjectivity, not single truth, is

the basis for the social reality under examination (Biesta & Burbules, 2003).

In practice, learning from individual cases was carried out in two ways:

through generalisation within and between the cases (Hammersley et al.,

2000; see also Huberman & Miles, 1994). In this research, these two ap-

proaches are considered as ways to draw the conclusions and to find plausible

explanations. Huberman and Miles (1994) suggest that generalisation within

the case is about describing what is happening, how it takes place and, espe-

cially, deriving an explanation for subjective experience, which is needed

when the research data does not cover the whole case in every detail. Ham-

mersley et al. (2000) indicate that the data-gathering period is normally rela-

tively short within discrete periods, or only a few people participate in the

research. However, the data is interpreted as part of a wider social reality. In

this research, for example, three separate data-gathering points through the

academic year were to cover the developmental process over the whole year.

However, the timing of these points was designed according to the structure

of the programme and, furthermore, individuals conceptualised their devel-

opmental process as a continuum during the programme. This was considered

during the data analysis as well as in the design of the interviews.

Generalisation across the cases is about the way to carry out analysis

through comparisons between the cases (Huberman & Miles, 1994; Ham-

mersley, et al, 2000). In order to be able to compare, the cases need to be


conceptualised at a more theoretical and abstract level. Developing the cate-

gorisation in order to form subsets in which the data fits nicely, but is still not

too general, is a challenge (Elo & Kyngäs, 2007). The development of cate-

gorisation here was established gradually through several cases starting from

the original themes based on the theoretical background. In the end, after

analysing several cases, the categorisation was reshaped to be applicable and

to address the research task. Only then were the differences and similarities

between individual cases possible to retrieve. Furthermore, it was possible to

build up a more general understanding of the developmental processes which

emerge in becoming a mathematics teacher within teacher education.

According to Elo and Kyngäs (2007), careful reporting is the way to in-

crease credibility of the research, to justify and to argue for the findings.

Only then is it possible to evaluate the strengths and limitations of drawing

research conclusions (see also Lincoln & Guba, 1985; Miles & Huberman,

1994). The researcher should explain how the results are derived from the

research data, in order to do which, data analysis needs to be reported care-

fully. In this research, detailed description of the procedure has been made,

starting from the case selection and ending with the elaboration of the data

analysis process. This description is supplemented by several appendices in

order to make the analysis process transparent. As Elo and Kyngäs (2007)

mention, describing the multiple phases of qualitative analysis process is de-

manding, but in this research, with the help of a systematic diary that the re-

searcher kept during the research procedure, it has been possible to follow the

process from the beginning to the end in retrospect.

In addition to careful description of the analysis process, the research

findings need to be structured and described in a way that transforms them

into an approachable and credible form for others. One practical challenge is

to make the report short enough but still not too compressed. In this report,

the link between the data and findings is established by authentic citations in

all cases. In addition, some content tables in the case displays help the reader

to get an overall view of each case (Miles & Huberman, 1994; Stake, 1995).

10.3 Transferability

Case study research has been accused of not being ‘scientific’ enough, espe-

cially in relation to the generalisability that is traditionally required in re-

search. However, ‘the real business of case study is particularisation, not

generalisation’ (Stake 1995, p. 8). Stake (2000) also comments that instead of

generalisation, the idea in case study is to expand the potential for experi-

176 Heidi Krzywacki

ences and to improve understanding of them. According to Hammersley and

Gomm (2000), the challenge of ‘generalisation’ has been addressed with the

discussion about transferability, naturalistic generalisation (Stake, 2000), and

comparison both across and within the cases, which was discussed here as

part of credibility (Hammersley et al., 2000; Miles & Huberman, 1994). One

possibility would be to uncover causal relations and argument underlying the

phenomenon in situ through eliminative and analytic induction (Patton, 2002;

cf. Hammersley et al., 2000). However, the starting-point would then neces-

sarily be in the existence of universal laws and regularities in the social

world, which is not particularly the case when discussing teacher identity.

Here, transferability addresses the need to consider the meaning of the re-

sults in any larger sense, i.e., whether the conclusions are transferable to

other contexts (Miles & Huberman, 1994; see also Flyvberg, 2006). It is not a

feature of the research but something that is manifested only when applying

the results in another context (Lincoln & Guba, 1985; see also 2000). The

researcher can enhance transferability through careful selection of the cases

that are typical and understandable within the research context (Hammersley

et al., 2000). Otherwise, the reader must assess the transferability of the find-

ings based on the research report.

Transferability is something that the researcher makes possible through

careful reporting. Elo and Kyngäs (2007) emphasise that since the readers

should be given an opportunity to consider the transferability of the findings,

the case displays need to be contextualised to allow the reader to consider

similarities and differences between the research context and the reader’s

situation (Stevenson, 2004). This research elaborates the context of the

teacher education programme as well as the individual cases in detail. The

description of the research procedure started with defining the cases and the

contextual features of the teacher education programme at the University of

Helsinki. The individual developmental processes make sense when the con-

textual features, such as the limited amount of teaching practice and oppor-

tunities to take a role as a mathematics teacher, are known. However, the

significance of different contextual features for individual experiences, or for

the developmental process cannot be shown easily. Besides, the process of

teacher identity formation is approached within the teacher education pro-

gramme in this research, with no immediate influence from the social interac-

tion that takes place in the school environment. This affects transferability of

the findings.

In addition to the description of the research context, there is a need to

make the research knowledge approachable and sharable through appropriate

conceptualisation (Stake, 1995; see also 2005: cf. Yin, 2003). The researcher


should consider pre-existing knowledge of the topic and differences in the

conceptual frameworks of the researcher and the readers. In this research,

building up the theoretical framework has been the way to conceptualise the

phenomenon and to make it comparable. However, transforming the research

knowledge into consistent form has been a challenge because of the various

conceptualisations of teacher identity available.

10.4 Dependability

Dependability is about whether the process of the study is consistent and

done with reasonable care (Miles & Huberman, 1994). Dependability affects

the overall research procedure, including methods used and decisions taken

during the process. The process should be reasonable and systematic to en-

sure that the data collection has yielded knowledge of interest and in accord-

ance with the purpose of the research (Stake, 1995). However, dependability

is not about being able to carry out the same research procedure with same

outcome at another time and place as would traditionally be the case with

reliability. In case study research, a systematic procedure is the way to ap-

proach the phenomenon in the intended way, especially through the interview

procedure (Seidman, 1998; Kvale, 1996).

Understanding the decisions made regarding the research procedure ne-

cessitates detailed description of the phases of the research as well as its con-

text (Schofield, 2000; Stake, 1995). One way to improve the quality of the

research is to pay attention to the data-gathering situations and to the overall

protocol of the empirical work (Miles & Huberman, 1994). The method-

ological issues and implementation of the research procedure have been dis-

cussed in detail in previous chapters. The data-gathering situations, such as

the social interaction with the research participants and setting, have affected

the insights gained (Keats, 2000; Seidman, 1998). The intention was to utilize

the interview situations with reasonable care.

First, the structure and the questions of the semistructured interviews

were carefully planned and tested; the student interview in a preliminary

study that took place a year beforehand and the teacher educators’ interview

in a rehearsal with a teacher educator not included among the research par-

ticipants. The concepts that the researcher used in the interviews were con-

sidered especially carefully in order to avoid leading questions (Warren,

2002).

Second, external factors might have influenced the data-gathering situa-

tions (see Kvale, 1996). The first interview situations in particular were

178 Heidi Krzywacki

something the students had not experienced before. Moreover, the discussion

and further information about the research project have probably stimulated

their awareness of their internal developmental process later in the process.

For example, the specific questions concerning their readiness as a teacher

might have prompted active reflection about their individual development.

However, even if this were the case, it is considered to increase the level of

conceptualisation, and therefore, to increase access to the phenomenon of

teacher identity formation. After all, the whole point of this research was the

idea that teacher identity formation may be examined through cognitive

stance and individual reflection (Beijaard et al., 2004). Besides, the influence

that the researcher had on the process was more like enhancing than altering

the development of the student.

Third, the interview situations were challenging, despite the researcher

having experience of such situations beforehand. Asking the questions and

introducing the themes for discussion without leading the interviewee was a

challenge. It was not only about concepts that the researcher brought to the

interviews but also the way different participants understood the terminology.

This challenge emerged with both students and teacher educators but not for

the same reasons. With the teacher educators especially, who represented

various university partners, the influence of the background discipline and

various perspectives needed to be considered in the interviews. In practice,

the differences were taken into account in dynamic interview situations with

the possibility of using follow-up questions included in the outline of the

interview (see Warren, 2002). Several interviews made it possible to revise

the details of the outline during the research. In addition to careful planning,

active attendance at the interview situations was strengthened by taking notes

during the interview and by trying to use concepts that the interviewee used

in his or her own reflection (Seidman, 1998). The reasons underlying the

statements were of particular interest.

According to Miles and Huberman (1994), prolonged engagement with

data sources is the way to avoid misunderstanding or misleading ideas in the

research (see also Lincoln & Guba, 1985). Since the data was dependent on

the students’ willingness to conceptualise their own developmental process,

the researcher was able to reconstruct this process only based on individual

experiences. The atmosphere in the interviews thus needed to be based on

mutual trust. The researcher wanted to avoid making any kind of judgement

or revealing her own conceptions of the issues under discussion. In addition

to a confidential relationship with the participants, different data sources and

multiple data-gathering points confirmed the researcher’s ability to make

sense of the developmental process.


When the interviews were carried out as planned, the interpretation of the

data became easier. Besides, it was helpful to be aware of different activities

provided in the teacher education and to consider the possible influences in

designing the two latter interviews with students. The teaching practice pe-

riods, the possibility of actually teaching, were seen as a fruitful starting-

point for reflections on the developmental process in general. The aim was to

take personal experiences as a point of departure for elaborating the under-

standing of developmental process.

10.5 Confirmability

The issues related to confirmability are ‘about relative neutrality and reason-

able freedom from unacknowledged researcher biases’ (Miles & Huberman,

1994, p. 278). The roles of the researcher (see Stake, 1995) have already been

described in more detail in the chapter about the case study approach, so that

the idea here is to summarise the influence that the researcher might have had

on the research procedure. Subjectivity can be seen as a characteristic of

qualitative research like this. Even if the procedure was carried out system-

atically and reported in detail, I have used my ‘backstage knowledge’ in the

interpretation process, both in carrying out the interviews and later in the

analysis phase (Seidman, 1998). I have been aware of my different roles in

relation to the research participants and within the context. The question is

whether the overall picture has been conveyed to the reader and the decision-

making and reasoning made explicit. In general, the various phases of the

analysis and reasoning have been reported in detail.

The subjective stance as a researcher has been influential for confronting

the overall view of the phenomenon. On the one hand, a person like me, who

is familiar with the research context, and who has experienced the process of

becoming a teacher, is more likely to be able to note essential features during

the research process. From this viewpoint, subjectivity means an opportunity

to identify with the role of the students involved with the developmental pro-

cess and to understand the viewpoints of the teacher educators. However,

subjectivity as a researcher might have led to bias in interpretation. Involve-

ment with cooperation in developing the teacher education programme and

personal experience has probably promoted sensitivity to the issues of indi-

vidual development, such as the meaning of practical experience. Unacknow-

ledged influences have been diminished by the theoretical knowledge influ-

encing the whole data analysis process and awareness of the different roles

that I have had as a researcher.


11 Discussion

The discussion is divided into four sections. First, the research purpose and

its practical implications are considered, second, the research findings and

conceptual framework in general; third, the implications for the teacher edu-

cation programme, and some remarks are made about contextual features

meaningful for teacher identity formation. Last, a few ideas for further re-

search are suggested.

11.1 On the relevance of the research

The basis of this instrumental case study research was pragmatism, as the

main research purpose emerged originally from practical experience. The

need to understand the process of becoming a mathematics teacher within the

teacher education programme was the primary research aim. The case study

approach was seen as a research method and strategy to reveal the nature of

the formation of emerging teacher identity (Stake, 1995). As Biesta and Bur-

bules (2003) state, some interplay between theory and practice is essential

when the research purpose is to foster understanding and provide practical,

better-informed practice. Since the criterion of relevance can emerge from

inside or outside the research field (Gellert, 2008), the research needs to be

appraised from two perspectives – how well the research purpose fits with its

context, and how well the study is linked to existing research knowledge of

the topic.

First, the relevance of using teacher identity as a central concept in this

research needs to be considered. The possibly restrictive feature of the

teacher education programme is the limited amount of teaching practice in-

cluded. The developmental process largely takes place through the imagina-

tion of the student, and is not especially promoted through practical class-

room experience. The absence of school experience and the role of the stu-

dent during the educational studies are somewhat problematic when discuss-

ing about teacher professional identity (cf. Walkington, 2005). After all, tak-

ing a role as a teacher gives a person the opportunity to see himself in teach-

ing profession and to experience interaction in the classroom (Danielewicz,

2001; see also Gee, 2000). However, the experiences, which promote the

individual developmental process and mediate socially shared views of being

a teacher are not simply those in the school environment. Even if students do

not have a real position as a teacher at school, they have different kinds of

182 Heidi Krzywacki

experience that are involved in the individual developmental process. A

teacher should possess expertise in different knowledge domains; for exam-

ple, mathematical knowledge that one does not learn through teaching.

Even if students have only slight experience of taking a role as a teacher,

and teaching practice periods do not simulate a real teaching position in a

school context, it is possible to conceptualise the process of ‘becoming a

teacher’ through teacher identity. This research was focused on the early

steps as a teacher, the beginning of the developmental process of teacher

identity formation. A student has opportunities to take a role as a teacher both

in real life as well as in imaginary thinking through various study tasks. Be-

sides, during the teacher education, a student should build up a solid base for

further development in school work, not only concerning the knowledge and

skills that a teacher should possess, but also commitment to the teaching pro-

fession and further development (see also Merenluoto, 2003). Altogether,

conceptualisation of the developmental process through teacher identity is

well reasoned, especially if identity formation is seen as a continuous process

that progresses in a teaching career at school as well.

Second, as Beijaard, Korthagen, and Verloop (2007, p. 105) state, under-

standing how teachers learn is essential for promoting teacher development.

They continue that answers to the question of understanding learning of

teachers may improve both initial teacher education and further professional

development of teachers. In this research, the focus was on teacher identity

formation in general, where learning has a significant role in seeking change.

The point of departure as well as the findings of the research have an inter-

face with educational reality. Furthermore, the research provides information

about individual development through conceptualised understandings, espe-

cially the early steps in becoming a teacher within the teacher education pro-

gramme. The features of Finnish teacher education have been taken into con-

sideration in the conceptual framework, especially those through which

teacher identity can be recognised and discussed. The most essential is the

conceptualisation of the process of becoming a teacher and, through that, to

highlight some meaningful points during teacher education.

Third, in building up understanding of teacher identity from the theoreti-

cal viewpoint, I have steered my way through a fragmented field of educa-

tional research and have tried to position the study in the conceptual frame-

work provided by recent research. Identity formation in general is a vast area

influenced by both the psychological and social sciences (Côté & Levine,

2002). Furthermore, when the concept of ‘identity’ has been applied to the

educational field to address the special features of teaching and learning,

those of the teaching profession particularly, the more complex the concep-

Discussion 183

tual basis has turned out to be. It was a challenge to clarify the assumptions

and to establish a theoretical framework based, at least to some extent, on the

variety of conceptual frameworks and approaches in the field. Choosing the

main concepts for the framework was particularly problematic. This research

cannot be considered to be foundational for conceptualisation of identity

formation in general; however, it does provide a modified perspective for

formation of emerging teacher identity by conceptualising what profession-

alism means for mathematics teacher identity and how the developmental

process takes place. Any attempt to build up a coherent picture of different

research strands is valuable.

11.2 Reflections on teacher identity formation

The present research was based on several premises. Firstly, teacher identity

is something that is recognized by ‘someone’ (Gee, 2000; see also Beijaard et

al., 2004) and, furthermore, this ‘someone’ is both a person, the one who is

becoming a teacher, and the others who are somehow involved with the pro-

cess within a social context (Côté & Levine, 2002; Danielewicz, 2001). Iden-

tity formation involves both external processes, which emerge from social

interaction in a particular context, and internal processes, which are related to

a personal self, as described in the social psychological framework of Côté

and Levine (2002). The interplay between a person and a context is thus es-

sential for the developmental process that takes place through giving meaning

to experiences. Secondly, as elaborated in the theoretical part of the report,

defining the concept of teacher identity through characterisation requires

stipulation of its associated aspects. In this research, subsets of cognitive and

affective aspects have been the basis for discussing teacher professional iden-

tity (e.g., Fajet et al., 2005). The individual state as a teacher and the devel-

opmental process may be recognised through the characteristics associated

with being a teacher. Besides, socially shared views of the profession may

also be elaborated through the individual aspects. Thirdly, teacher identity

formation is also considered as an on-going process, a dynamic entity (Dan-

ielewicz, 2001; see also Beijaard et al., 2004; Richardson & Placier, 2001).

However, one’s state as a teacher may be captured by the person involved

and by others through observing the way teacher identity is manifested at the

personal identity level (Côté & Levine, 2002). Since this makes the state of

teacher identity recognisable, experiences promote understanding of teacher

identity through given meanings.

184 Heidi Krzywacki

The process of teacher identity formation is seen here as a series of chan-

ges towards being a good teacher, which is mediated by experience. The

meaning of a continuum of experiences in the developmental process em-

erged alongside the theoretical review (see Samuel & Stephens, 2000). The

Deweyan idea of a continuum between past and future mediated by present

experience is seen here as essential. The experiences that an individual has in

social interaction within a given context promote teacher identity formation.

The significance of various events depends on the person and his/her under-

standing of what has been internalised through previous experience (Côté &

Levine, 2002; see also Sfard & Prusak, 2005). The image of the ideal teacher

is seen here to pave the way for individual development, as in the work by

Arnon and Reichel (2007) (cf. Sfard and Prusak, 2005). The image of one’s

present state as a teacher (How am I as a teacher at the moment?) and the

image of the ideal teacher (How would I like to be as a teacher?) are crucial

to the developmental process (see also Beijaard et al., 2004). From the indi-

vidual perspective, teacher identity formation is about reflecting on one’s

present state as a teacher through experience in social interaction. Besides, it

is about becoming aware of one’s personal view of a good mathematics

teacher and, depending on individual commitment to the developmental pro-

cess, aspiring towards a desirable state as a teacher in the future (see Krzy-

wacki-Vainio & Hannula, 2008). The formation of teacher identity is possible

to capture through conceptualisation of understandings.

An individual has an active role in constructing professional identity as a

mathematics teacher within the context (see e.g., Coldron & Smith, 1999;

Danielewicz, 2001). The idea in this research was to construct a conceptual

framework for analysing emerging teacher identity and its formation based

on characterisation, the images of the present and ideal state as a teacher, and

the idea of the on-going process. In practice, as was the case with Mary and

John, the individual state of teacher identity was elaborated at two levels, the

present and the ideal images. The profile of the state as a teacher was possible

to scrutinise through the affective and cognitive aspects associated with being

a teacher at both levels. The formation process and changes could be exam-

ined based on the three data-gathering points. Altogether, it seems that an

individual constructs own way of being a teacher first at the ideal image

level, and then gradually identifies with the teaching profession at the present

level (cf. Arnon & Reichel, 2007). In the context of Finnish academic teacher

education in particular, becoming a professional mathematics teacher is not

merely about taking the obligatory studies but also envisioning a personal

way of being a teacher. Awareness of the image of the ideal teacher, espe-

cially of desirable characteristics, is essential. Gradually, with educational

Discussion 185

studies and practical school experience, students internalise their role as a

teacher and begin to feel like a ‘real’ one. At this point, being a teacher is not

only a matter of a designated state but also the present state of teacher iden-

tity (Sfard & Prusak, 2005).

However, the developmental process is not straightforward and, as em-

erged from the cases of John and Mary, discrete aspects of the ideal math-

ematics teacher do not automatically direct the individual development. This

ideal image directs identity formation only if it is linked with an individual

process (Arnon & Reichel, 2007). The width of the gap between the present

and the ideal image is significant. The ideal image directs the developmental

process as if it is something attainable from the viewpoint of the present state.

Moreover, an individual needs to be engaged with the developmental process

and to set personal goals on the basis of the ideal image. In fact, it was shown

that the ideal image directs and is linked to the personal developmental pro-

cess differently, depending on each characteristic. The ideal image is con-

structed through a range of characteristics, from which the personal develop-

mental goals emerge. The view of the present state as a teacher influences an

individual and creates prioritisation of personal goals, i.e., concentrating on

shortcomings that need to be improved. The conceptual framework lacked the

level of personal developmental goals, something through which the ideal

image would have been mediated as part of an individual process.

The individual developmental process is promoted by social interaction

and the experiences that mediate socially shared ideas of being a mathematics

teacher. An individual manifests his or her state as a teacher in interaction

with others in particular situations, so that others influence the formation pro-

cess (Côté and Levine, 2002). Danielewicz (2001) calls this ‘going public’. In

teacher education, the individual has an opportunity for interaction and for

getting feedback in the teaching practice lessons, indirectly and intentionally.

The self-presentation of teacher identity, as well as recognising one’s state as

a teacher is accessible through characteristics associated with being a profes-

sional teacher, for example, the fields of expertise that a good mathematics

teacher should possess. While an individual has become aware of socially

shared ideas of being a mathematics teacher in the Finnish school system,

s/he tries to fulfil the expectations of a real teacher at the interactional level,

the feedback in social interaction being based on recognisable characteristics

apparent in individual behaviour. The boundaries between what is individual

and what is socially shared are of interest. The view of an individual and the

socially shared view of being a teacher should converge sufficiently to pro-

duce feedback that promotes professional development in that context. After

all, the question is not only about individual development and the view of

186 Heidi Krzywacki

being a teacher, but also about the need to be recognised as a professional by

others and to attain a position as a ‘real’ teacher (cf. Gee, 2000). The range of

characteristics does not need to be exactly the same, as was the case in this

research, but individual and socially shared views need to overlap enough in

order to fulfil the requirements as a believable professional.

However, in academic teacher education, like the context of this research,

the opportunities to teach in the classroom and to manifest one’s state as a

teacher are limited. The process of becoming a mathematics teacher is not

mainly guided by teaching experience situated in ‘real school life’ but largely

by the academic learning processes. Student teachers thus need to be able to

use their imagination to identify themselves as teachers during their academic

studies. For example, neither the students nor the teacher educators high-

lighted practical skills associated with becoming and being a good mathemat-

ics teacher, possibly because of limited teaching practice experiences in-

cluded in the programme. The ideal image level is seen as essential to the

individual developmental process, as well as the boundary between individ-

ual, internal processes and social, external processes during teacher education

(see Danielewicz, 2001). The ideal image is the level at which individual and

social interface. Student teachers become acquainted with socially shared

conceptions of a good teacher through social interaction with others, reshap-

ing their own personal understanding of being a teacher by filtering socially

shared ideas, and aspiring to manifest them at the interactional level (Beijaard

et al., 2004; Côté & Levine, 2002).

The title of this study is about emerging teacher identity, which raises the

question of attaining the state of being a ‘real’ teacher. Here, the main re-

search task concerning the process of teacher identity formation during the

teacher education programme has been approached from both individual and

social perspectives. The emphasis has been on the role of an individual who

is seen as an active subject who constructs a professional identity within a

given context (e.g., Beijaard et al., 2004). As Bohl and van Zoest (2002)

point out, the existence of teacher identity is dependent on both individual

and social views. On the one hand, an individual needs to internalise a role as

a teacher, and begin to feel like a real professional through fulfilling the char-

acteristics that s/he associates with being a teacher. On the other hand, in

addition to individual feelings about one’s state as a teacher, the others need

to consider a person as a teacher (Brown, 2003; Walkington, 2005). Only

when these two requirements are met does teacher identity supersede taking a

role as a teacher. This research concerns the early steps of developmental

process of formation of teacher identity and, depending on individual experi-

Discussion 187

ences and motivational background, students are in different phases of their

process when they graduate from the university.

The subsets for collection of characteristics are one way to approach

teacher identity in a particular context (see Beijaard et al., 2004). These char-

acteristics were the way to describe what it means to become and to be a pro-

fessional mathematics teacher, particularly in the Finnish educational system.

However, although the various characteristics of a good teacher could be ap-

plied to other educational contexts, the emphasis and possibly the rationale

underlying the desirable characteristics differ according to context. In this

research, the social view of teacher identity was defined through affective

and cognitive aspects that emerge from the teacher education curriculum as

well as from the perspective of each teacher educator. There are several ways

to establish the framework for these characteristics, and the researcher’s own

understanding, influenced by practical experience and educational research,

has had an influence on the structure. Expertise in thinking skills and the

ideal of a teacher as a researcher are important in academic teacher education

in Finland. The autonomy of a professional teacher and the idea of different

kinds of good teachers are seen as characteristics of the Finnish educational

system (Lavonen et al., 2007). In this research, individual students seemed to

identify with the idea of an autonomous status as a teacher, as well as the

need for constituting one’s own way of being a professional teacher. How-

ever, ‘a teacher as researcher’ was not associated with the image of being a

good teacher. Individual views did not converge with the socially shared

view, even if the idea of ‘a teacher as researcher’ is greatly stressed in the

study programme. No further conclusions can be drawn here based on so few

cases, but general discussion could be a desideratum.

11.3 Implications

The relevance of this study is its connections with the context and possible

applications for developing the study programme. As Younger et al. (2004)

state,

the challenge for teacher educators is to frame teacher education courses in such

a way that beginning teachers are provided with the contexts and methodologies

whereby they can reflect upon their own preconceptions and refine their own un-

derstandings as to how they themselves learn as teachers, to enable them in turn

to facilitate the learning of pupils and to fulfil their own clearly articulated aspi-

rations to become quality teachers (p. 262).

188 Heidi Krzywacki

From the perspective of teacher education, the interplay between external and

internal processes of teacher identity formation is of specific interest in con-

sidering implications for aspiring for more intelligent practice (see Biesta &

Burbules, 2003). In practice, the main question is not only what we should

offer within the programme but also how we should implement the studies.

The need for experience as a teacher in the classroom emerged in the re-

search findings. The teaching practice periods during teacher education pro-

vide an opportunity for a student to take a role as a teacher, even if not on a

large scale (cf. Danielewicz, 2001). Naturally, a greater amount of teaching

practice lessons would make it possible to engage with social interaction, and

furthermore, to get feedback on the manifested state as a teacher. However, a

student could not have a real position as a teacher during the pre-service

teacher education in any case. Such a position is possible only in full em-

ployment in the school context, while in the research findings, it was the

greatest deficiency of the programme. First, taking a role as a teacher was

meaningful for the developmental process because of the possibility to clarify

the view of oneself as a teacher. For example, the meaning of different know-

ledge domains might change as a result of practical experience. Furthermore,

in order to enhance the process of becoming a teacher from the beginning of

the programme, students could benefit from teaching experiences before

graduation from university, usually during the last academic year. The con-

straint is that students have to complete enough courses in mathematics and

in another school subject to ensure a level of content knowledge and skills

before entering teaching practice.

Second, practical experiences are not only important because of taking a

teacher’s role and being able to see oneself in the teaching profession. The

feedback that a student gets from teaching practice lessons as well as from

cooperative activities with other students strengthens the view of oneself both

in terms of the present and the ideal image. Teacher educators, sometimes the

other students in teaching practice schools as well, provide useful feedback

for further reflections and may guide the process. The ideal image that is me-

diated in the teaching practice should be considered carefully, not only from

the viewpoint of the school system and practical requirements as a teacher

but also for augmenting the academic work. The idea of research-based

teacher education including theoretical studies in educational sciences espe-

cially should emerge somehow in practical work. Students sometimes miss

the link between theoretical studies and practice (Gore & Gitlin, 2004). Be-

sides, discussions during the teaching practice periods usually relates to a

personal developmental process that involves affective aspects in addition to

the knowledge and skills needed as a teacher (Korthagen, 2007).

Discussion 189

Academic cognitive skills and knowledge are strongly emphasised in the

programme, in which the solid foundation for becoming a teacher is math-

ematical knowledge and skills (see Lavonen et al., 2007). A teacher is re-

garded as a professional who is an expert in teaching and learning mathemat-

ics, beside competence for further development later in the teaching career.

From this viewpoint, mathematical content knowledge provided during the

pre-service education programme is probably a good starting-point for pros-

pective mathematics teachers (Ferrini-Mundy et al., 2007). Still, the need for

a coherent view of mathematics and understanding the nature of mathematics

as a school subject should be taken into consideration during the programme.

Especially in mathematical education, it might be hard for students to under-

stand intentions and the meaning of subject matter studies for their future

profession (D. Cohen, 2008). It is not a new idea that among the university

mathematics courses students should have an opportunity to build up a link

between academic mathematics and school mathematics for gaining math-

ematical knowledge (e.g., Ball and Bass, 2000). Furthermore, combining

studies in education and practical experiences with strong mathematical back-

ground is a challenge.

The courses in different knowledge domains are seen as an important part

of becoming a teacher. The process is not only about taking a role as a

teacher and about ‘learning by doing’, as the competence that a teacher

should possess as a professional is gained through academic studies (cf. Hie-

bert et al., 2002). However, it is a challenge to support students in building up

an overall picture of being a mathematics teacher and to integrate all these

competences together. Teacher education can be seen as a learning envi-

ronment for students to develop themselves autonomously as a teacher, but

the active support of teacher educators is still needed at various levels

(Korthagen, 2004). In order to be able to support students in their develop-

ment, a coherent view of being a mathematics teacher should be provided in

the study programme. The differences between the written official curriculum

and implementation of the programme should be given particular attention.

For example, it seems that teacher educators emphasise subjective viewpoints

of becoming a teacher, like self-confidence as a teacher, during the teacher

education programme. However, the hidden agenda is a challenge for further

development of the programme as the implementation of the programme va-

ries from one educator to another.

Lastly, understanding the individual formation of teacher identity is

meaningful for implementing teacher education in such a way that different

aspects of teacher identity formation can be addressed. Academic teacher

education seems to fail to support student teachers in combining affective and

190 Heidi Krzywacki

subjective aspects with academic knowledge and skills in the best possible

way (cf. Eteläpelto & Vähäsantanen, 2006; Beijaard et al., 2004). Orienting

student teachers toward personal development during their educational

courses is a special challenge after theoretical studies in mathematics (see

also Krzywacki-Vainio, 2009). However, support for personal development

is not necessary in relation to face-to-face interaction between students and

teacher educators. For example, interaction with other students and enhancing

self-reflective activities during the programme are also a useful way to pro-

mote individual development and benefit from social interaction.

11.4 Further research

Some ideas emerged during the research about the potential and need for fur-

ther research. First, since this research was on the developmental process of

becoming a mathematics teacher, the role of mathematical content knowledge

arose in the data. However, as Reid et al. (2008) mention, the role of disci-

plinary knowledge varies between fields. The conceptual framework with

separate characteristics, based on which professionality as a teacher was dis-

cussed from the individual and social perspective, might be applied to other

kinds of teachers. It would be interesting to elaborate more carefully the

meaning of expertise in different content knowledge areas, for example, with

secondary teachers in different school subjects or with elementary school

teachers (cf. Hodgen & Askew, 2007; Smith, 2007). Moreover, while the

profile of teacher identity differs between individuals, the question would be

about the features that are particular for teacher identity in different areas.

Second, this research is primarily concerned individual developmental

process within the teacher education programme. The features of the individ-

ual process were highlighted, and contextual, external processes remained

peripheral. It would be interesting to understand the mechanisms in the de-

velopmental process from a social perspective better. Like the original the

idea in this research, evaluative study of the teacher education programme

and its contextual features and for developing the programme could be of

use. Moreover, the influence of the school context as well as cultural differ-

ences between educational systems might reveal some interesting aspects.

Thirdly, the individual developmental process was approached through

interviews and written documents but not through the meaning-making of

particular experiences in the classroom, for example, observing interactional

situations in which self-presentation of teacher identity takes place and dis-

cussing this particular situational experience. The process of teacher identity

Discussion 191

formation could already be seen in a new perspective during the teacher edu-

cation programme when manifestation of the state as a teacher, i.e., actions in

the classroom, and elaboration of manifestations could form part of data-

gathering. The influence of others and through that the contextual influence

on the formation process could then be handled in more detail. However,

understanding of the cases could emerge from practical experience, so that

the examination of emerging teacher identity need not be based simply on

conceptualisation of research participants in general.

Last, this research focused on the early steps of the process of teacher

identity formation, on emerging teacher identity. The process of becoming a

teacher continues in the school environment, through practical experience in

a teaching position (McCormack et al., 2006). The plan is that the follow-up

research is going to examine the meaning of school experiences and monitor

the developmental process of the former students who participated in the re-

search. Only then can something be said about the interplay between the

school context and an individual, and about the continuum of experience.


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Appendices

Appendix 1. Information letter for the student teachers

A letter and an opportunity for enrolment that was distributed to all math-

ematics student teachers in the first portfolio assessment meeting (August

2005).

Research on mathematics teacher education

Dear recipient,

I am conducting research on mathematics teacher education. The focus of the

research is on becoming a teacher and the formation of teacher knowledge

during the teacher education programme. Both teacher educators’ and student

teachers’ viewpoints are taken into consideration in the research.

I am searching for students willing to be research participants, who are plan-

ning to complete their educational courses largely or entirely during the

2005–2006 academic year. Those who participate in the research will be in-

terviewed three times during the academic year.

Naturally, all data and information related to the research will be handled

confidentially and anonymously.

Thank you for your co-operation,

Heidi Krzywacki

P.O. Box 9 (Siltavuorenpenger 20R), room 308a

E-mail: [email protected], Gsm. (041) 532 0235

204 Heidi Krzywacki

Appendix 2. Information letter for the teacher educators

Research on mathematics teacher education

My research is about mathematics teacher education and the development of

student teachers during the programme. The focus of the research is on be-

coming a teacher and the formation of teacher knowledge during the teacher

education programme. Both the perspectives of the teacher educators’ and

student teachers are taken into consideration in the research.

In this research, all university teachers responsible for the courses included in

the teacher education programme for mathematics student teachers are re-

garded as teacher educators. Teacher educators represent three different part-

ners; the Department of Applied Science of Education, the Department of

Mathematics and Statistics, and university teaching practice schools. Re-

search participants representing the viewpoint of teacher educators should be

key persons in the programme to some extent. In practice, such a teacher

educator should be both, an active partner in planning and developing the

study programme and responsible for course implementation as a part of the

programme. Besides, the selection is also based on the structure of the pro-

gramme and study arrangements during the 2005–2006 academic year.

I would be pleased to have you as one of the research participants. The inter-

view will last approximately two hours and the plan is to complete the inter-

views in April or May in 2006. The interview will be audiorecorded and,

naturally, all data and information related to the research will be handled con-

fidentially and anonymously.

It would be really nice if you could participate in the research. We can talk

about the research and I can give further information on the phone – I’ll con-

tact you later.

Thank you for your co-operation,

Heidi Krzywacki-Vainio

P.O. Box 9 (Siltavuorenpenger 20R), room 308a

E-mail: [email protected], Gsm. (041) 532 0235

Appendices 205

Appendix 3. Background information of the student teachers

Some basic information was obtained at the first meeting.

• Name:

• Age:

• Experience in being a (substitute) teacher:

• When did you start at university? When were you accepted for the

teacher education programme? When did you start the educa-

tional studies?

• Major subject (first school subject) and phase of your studies in

autumn 2005

Are there specific courses for student teachers included in your

studies?

If so, what kind of course and how many study points?

• Minor subject (second school subject) and phase of your studies in

autumn 2005

Are there specific courses for student teachers included in your

studies?

If so, what kind of course and how many study points?

• Study history and any previous degree

• Have you completed some educational courses before

the 2005–2006 academic year?

If so, in which university and what kind of courses? How many

study points?

206 Heidi Krzywacki

Appendix 4. The themes of the first interview with the student teachers (au-

tumn 2005)

Possible follow-up questions marked with italics.

Start Tell me about your study history.

When did you start at university?

What about the educational studies that you have just started…?

Motivational background for becoming a teacher What are your reasons for becoming a teacher and for completing the teacher edu-

cation programme?

When did you make the decision about your future career?

Expectations and aims for the programme Tell me about your expectations of the teacher education programme.

…specific contents? …study arrangements? …methods?

What goals you have set for your studies?

Conceptions of teaching and learning mathematics Describe briefly your own experiences in school mathematics.

What were your mathematics teachers like?

What was it like to study mathematics?

Describe what a good mathematics teacher is like.

Explain why the issues or features that you mentioned are relevant.

What kind of mathematics teacher would you like to be?

Why?

Teacher knowledge and skills What is the best way to evolve into a good teacher like the one you described?

What kind of knowledge and skills beside experience could teacher education

provide for development?

How would you like to develop yourself as a prospective teacher?

Self-assessment on strengths and weaknesses

What goals have you set for your studies? (question repeated)

What might be most challenging for you during the programme?

Reflect on the best way for you to learn new things and skills.

Appendices 207

Appendix 5. The themes of the second interview with the student teachers

(December 2005)


Start How have your studies been going during this academic year?

What courses have you completed?

Expectations and aims for the programme [Summing up the issues emphasised in the previous interview in autumn 2005.]

Have your expectations and goals for the studies been fulfilled?

What about the relevance of your expectations and goals at the beginning…?

…specific contents? …study arrangements? …methods?

Has something unexpected surprised you?

Conceptions of teaching and learning mathematics Describe what a good mathematics teacher is like.

Explain why the issues or features that you mentioned are relevant.

What kind of mathematics teacher would you like to be?

Why?

How has your view of being a teacher changed during your studies?

Teacher knowledge and skills What kind of knowledge is required as a subject teacher?

What kind of skill is required as a subject teacher?

Give reasons for your views.

How would you like to develop yourself as a teacher?

Some self-assessment on strengths and shortcomings

Relevance of the teacher education programme What kind of knowledge and skills has the programme provided so far?

How has the programme supported your development as a teacher?

What kind of goals have you set for your studies in future?

208 Heidi Krzywacki

Appendix 6. The themes of the third interview with the student teachers

(spring 2006)


Start How have your studies been going during the academic year?

What courses have you completed and when are you going to graduate?

Expectations and aims for the programme Have your expectations and goals for the studies been fulfilled?

Has something unexpected surprised you?

New viewpoints…?

Conceptions of teaching and learning mathematics What is essential in teaching and learning mathematics in your opinion?

Assess yourself as a mathematics teacher (knowledge and skills)

Some self-assessment on strengths and shortcomings

How would you like to develop yourself in future?

What is most challenging for you in being a teacher?

How has your view of being a teacher changed during the past year?

Relevance of the teacher education programme Describe three essential features of the teacher education programme for a new-

comer.

What has the programme provided for you as a prospective teacher?

Describe the essential goals for the programme.

How well have the goals been achieved in your case?

What image of being a teacher was provided in the programme?

How has the programme supported your development as a teacher?

What is the role of … (separate sections of the programme mentioned by the

interviewer)

In what way has the background of students been taken into consideration

during the programme?

Assess how your subject studies in mathematics has allowed you to gain readiness

for being a teacher.

How would you develop the teacher education programme?

Something that you were missing…?

What would you like to maintain?

Something irrelevant…?

What are your plans in future as a teacher? Where would you like to work as a

teacher?

Appendices 209

Appendix 7. The themes of the interview with the teacher educators


Start Tell me about your background as a teacher educator.

How did you become a teacher educator? Your remit in the subject teacher

education programme…?

Conceptions of teaching and learning (mathematics) Describe what a good subject (mathematics) teacher is like.

Why? In what way have your conceptions changed over the years?

Role of the subject (mathematics)

Knowledge and skills of a subject (mathematics) teacher What kind of knowledge (methodological, contentual) is required as a subject

teacher?

What skills (methodological, contentual) are required as a subject teacher?

Relevance and objectives for subject teacher education Describe the essential goals of your course and how these are implemented.

Methods used in the course? Planning process?

What specifically supports individual development as a teacher?

What are your strengths as a teacher educator? How would you like to de-

velop yourself?

How are the goals achieved during the course which is your responsibility?

Your notions on students’ attitudes, learning…?

What are the main goals of the teacher education programme?

According to you, the most relevant in the programme?

Something that isn’t so relevant…?

How well are the goals of the entire programme achieved?

What is the most challenging part of teacher education?

In future How should the programme be developed?

What skills and knowledge should the programme provide for students?

Special experiences? Particular contents or methods?

Study arrangements

Describe your own role as a teacher educator.

What is the meaning of co-operation with other teacher educators for you?

210 Heidi Krzywacki

Appendix 8. The first version of data categorisation (student cases)

A point of departure and background of the prospective teacher Reasons for becoming a teacher and participating in the study programme

A point of departure as a student

your own school experiences

experience as a teacher

educability/suitability as a student

Conceptions of good mathematics teaching and the teaching profession Features of a teacher

knowledge

skills

attitude

Teaching mathematics

Identification as a teacher How does a student identify his- or herself as a teacher?

How is the level of commitment in being a teacher?

View of self as a teacher

Motives for applying for the programme

The ideal teacher

Identification with being a teacher / socialisation with school community

The feeling of being a teacher (self-assessment)

Expectations and aims for the teacher studies How have your personal aims change during the year of educational studies?

Evaluation of the studies

How does a student find the studies regarding his or her own developmental pro-

cess?

How does the programme support individual development as a teacher?

studies in university mathematics

studies in mathematics education

studies in educational sciences

teaching practice periods

practical study arrangements

portfolio assessment work

Something to be developed further

Discussion on some other matters (start, ending)

Appendices 211

Appendix 9. The second version of data categorisation (student cases)

Numbering was used for coding during the analysis.

Conceptions of teaching and learning (ideal and self-assessment)

Code

General conceptions, e.g., of pedagogi-

cal thinking 100

Conceptions of the teaching profession 101 Cognitive aspects

generally 110 Mathematical content knowledge

personal readiness 111 generally 120 Pedagogical content knowledge (PCK):

about teaching mathematics personal readiness 121

generally 130 Pedagogical knowledge and skills (PK):

e.g., relationship with pupils personal readiness 131 generally 140

thinking skills and self development personal readiness 141

Affective aspects

generally 150 Personal features (attributes and social

interaction) personal readiness 151 Affective aspect: attitude towards teach-

ing profession, willingness for devel-

opment

generally 160

School as societal institution (context

outside the classroom) 170

generally 180 Routines and classroom situations (ex-

perience, authority?), implementation personal readiness 181

“I am going to be a teacher”

Code

Background Previous learning (school) experiences 200 previous studies 201

oneself as a learner and as a student 202

Work experience 210

212 Heidi Krzywacki

Motives for applying for the pro-

gramme: choice of career 220

Development during the course Commitment to self development 230

changes in thinking and conceptions

(conscious) 231

developmental process (internalisa-

tion of new knowledge and skills) 232

Feeling of being a teacher (identifica-

tion) 240

taking a role as a teacher (practice) 241 In future (commitment to the teaching

profession) 250

How does the programme support individual development?

Code

Orientation towards the studies: expec-

tations and personal goals 400

practical study arrangements (such

as information)

new ideas

Mathematical education 410

The educational studies

Conceptions of various disciplines

(differences) 415

Meaningfulness of the studies, attitude

towards the studies

one’s own expectations juxtaposed

with the aims of the programme 416

Mathematics education minor educational thesis 420 special needs education

social, historical, and philosophical

basis for education Studies in educational sciences

psychology of development and

learning

430

Teaching practice periods 440 Reflection and thinking skills (portfolio

assessment work) 450

Studies in general 460 Ideas for further development (in gen-

eral) 470

Social interaction within the studies 480

Appendices 213

Appendix 10. The third version of data categorisation (student cases)


Conceptions of teaching and learning

Code

General conceptions of teaching and

learning 101

School as societal institution

(context outside the classroom) 170

The teacher as an individual

Code

General conceptions of being a teacher,

e.g., of pedagogical thinking 110

Cognitive aspects



about teaching mathematics personal readiness 121

generally 130 Pedagogical knowledge and skills (PK):

e.g., relationship with pupils personal readiness 131 generally 140

Thinking skills and self development personal readiness 141

generally 180 Classroom implementation

(routines and classroom situations) personal readiness 181 Affective aspects

generally 150 Personal features (attributes)

personal readiness 151 generally 160 Attitude towards teaching profession,

willingness for development personal readiness 161

214 Heidi Krzywacki

“I am going to be a teacher”

Code

Background Previous learning (school) experiences 200 previous studies 201

oneself as a learner and as a student 202

Work experience 210

Motives for applying for the pro-

gramme: choice of career 220

Development during the course Commitment to self development 230

changes in thinking and conceptions

(conscious) 231

developmental process (internalisa-

tion of new knowledge and skills) 232

Feeling of being a teacher (identifica-

tion) 240

taking a role as a teacher (practice) 241

Commitment to the teaching profession

in future 250

The study programme and implementation

Code

Meaningfulness of and attitude to-wards the course

Orientation towards the studies: expec-

tations and personal goals 400

conceptions of various disciplines

(differences) 415

One’s own expectations juxtaposed

with the aims of the programme 416

New ideas 402 The role as a learner: individual devel-

opment 403

Relation of theory and practice 404

Study implementation

Practical study arrangements (e.g.,

information) 401

Study performance and activities (e.g.,

reading) 407

Social interaction within the course 480

Appendices 215

Different sections of the programme Mathematical education Educational studies minor educational thesis mathematics education 420

special needs education


basis for education Studies in educational sciences


learning

430

Teaching practice periods 440 Reflection and thinking skills

(portfolio assessment work) 450

Evaluation of the programme The programme in general 460 Ideas for further development

(the programme in general) 470

216 Heidi Krzywacki

Appendix 11. The final version of data categorisation (student cases)


Conceptions of teaching and learning mathematics

Code

General conceptions of teaching and

learning 101

Teaching and school organisation in

general 170

Individual teacher and teacher com-petences

General ideas related to being a teacher,

e.g., of pedagogical thinking 100

Cognitive aspects related to being a mathematics teacher



teaching and learning mathematics personal readiness 121

generally 130 Pedagogical knowledge and skills (PK)

personal readiness 131 generally 180 Knowledge and skills for classroom

implementation personal readiness 181

generally 140 Thinking skills and readiness for self-

development personal readiness 141 Affective aspects related to being a mathematics teacher

generally 150 Personal characteristics of a teacher

(attributes) personal readiness 151 generally 160 Attitudes towards the teaching profes-

sion and willingness to develop personal readiness 161

Appendices 217

Personal process of becoming a teacher

Code

Background of a prospective teacher

Learning experiences and school at-

tendance

200 201

202

Teaching experience 210

Motives for applying for teacher educa-

tion 220

Individual developmental process Self-development in teacher education 230 Identifying with being a teacher 240

Self-confidence as a teacher 242

Acting as a teacher and learning at work 241 Commitment to the teaching profession

in future 250

Teacher education supporting the individual development

Code

Meaningfulness of and attitude to-wards the course

Personal aims alongside the aims of the

study programme 416

Orientation toward the course (per-

sonal aims and expectations) 400

Conceptions of mathematics and educa-

tion as a discipline 415

Added value of the course (new ideas) 402 Individual process and consideration of

personal background 403

Combining theory with practice 404 Content and implementation of the course

Courses in university mathematics

(mathematical education) 410

Educational studies Mathematics education 420

Educational research seminar (mi-

nor thesis) 421

218 Heidi Krzywacki

General educational studies 430 special needs education 431


basis for education 432


learning 433

Supervised teaching practice 440 Teaching practice I (basic module) 431

Teaching practice II (applied mod-

ule) 432

Teaching practice III (advanced) 433

Portfolio assessment work 450 The overall view of the course Practical study arrangements 401 Studying and methods used in the pro-

gramme 407

Social interaction within the course 480

Appendices 219

Appendix 12. The first version of data categorisation (teacher educators)


Code

Role as a teacher educator 100 Position in the study programme and

responsibilities 110

Background and motivational back-

ground 120

Research interests 130

Strengths as a teacher educator:

personal image 140

Need for further development 150

Relations with students 160 Relations with other teacher educators

within the programme 170

Conceptions of teaching and learning mathematics (ideal) 200

Image of the ideal teacher and good

teaching

Knowledge (the role of school

subject); skills (interactional skills);

personal features; affects; develop-

ment of the school organisation;

becoming a good teacher?

210

Special issues in being a teacher 220 Change in one’s own views 230 One’s own course(s) as a part of the programme

300

Aims and essential content 310 Planning process 320 Implementation of the course 330

Characteristics of student teachers

(background, differences between

disciplines)

340

Assessment of the course implementa-

tion: aims 350

Special support for formation of teacher

identity 360

Notions about students and their learn-

ing outcomes 370

220 Heidi Krzywacki

The overall view of the study pro-gramme

Aims and entrance examination 410 Assessment of the programme: the

significance for individual development 420

Idea for further development: in general

and for one’s own course 430

Changes regarding the programme:

renewal of the study programme 440

Appendices 221

Appendix 13. The second version of data categorisation (teacher educators)



Code

Role as a teacher educator 100 Background and motives for being as a

teacher educator (educational back-

ground)

110

Position in the study programme 120

Research interests 130 View of self as a teacher educator 140 Strengths and shortcomings 141

Relationships with other teacher educa-

tors 150

Conceptions of good teaching and learning (in mathematics) 200

Image of the ideal (subject) teacher and

about good teaching 210

content knowledge and skills 211

pedagogical content knowledge

(learner’s perspective) 212

pedagogical knowledge; e.g., rela-

tionship with pupils, motivation 213

personal features (attributes, social

skills) 214

affective aspects: attitudes towards

the teaching profession, willingness

for self-development

215

Special issues in being a teacher 220 School as an organisation and organisa-

tional development 230

Change in one’s own views 240 Views of mathematics as a discipline

(special features) 250

222 Heidi Krzywacki

Implementation of the teacher education programme

Code

One’s own course(s) as part of the programme

300

Aims and essential content 310

Special support for formation of

teacher identity 311

Planning process 320 Implementation of the course 330 Assessment of the course implementa-

tion

Notions about students and their

learning outcomes 340

Ideas for development 350 Relations with students (generally) 360

Characteristics of student teachers

(background) 361


400

Aims of the programme and essential

content (entrance examination) 410

Assessment of the programme: its sig-

nificance for individual development 420

Idea for further development in general 430 Changes: renewal of the study pro-

gramme 440

Appendices 223

Appendix 14. The final version of data categorisation (teacher educators)



Code

Role as a teacher educator 100 Background as a teacher educator 110 Educational background 111

One’s own school and learning

experiences 112

Work experience 113

Position in the study programme 120 Research as a part of the work 130 Conceptions of oneself as a teacher

educator 140

Strengths and needs for further

development 141

Relationships with other teacher educa-

tors within the programme 150

Conceptions of mathematics as a disci-

pline in general 160

Conceptions of good teaching and learning (in mathematics)

Image of the ideal teacher General ideas related to being a teacher 210 Cognitive aspects

content knowledge 211

pedagogical content knowledge 212

pedagogical knowledge 213

Affective aspects related to being a

teacher

Personal characteristics of a teacher 214

Attitudes towards the teaching

profession 215

Teaching and school organisation in

general 220

Changes in one’s own conceptions of

teaching and learning 230

224 Heidi Krzywacki

Implementation of the teacher education programme

Code

One’s own course(s) as part of the programme

Aims and essential content 310

Special support for formation of

teacher identity 311

Preparation and planning of instruction 320 Implementation of the course 330 Assessment of the course 340 Ideas for further development 341

Relationship with students in general 350 Characteristics of student teachers 351


Aims and essential content 410 Motivational background of student

teachers and application procedure 420

Assessment of the programme: its sig-

nificance for individual development 430

Ideas for further development 440 Changes regarding the programme 450

becoming a teacher: emerging teacher identity in

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